Student Voices Episode 3: Chris, Craig, and Graeme

In this episode of Student Voices three Advanced Placement Calculus students, Chris, Craig, and Graeme, talk about a wiki assignment they did to prepare for the exam. Then the conversation transitions to a discussion of the many things they learned while doing their Developing Expert Voices project. It ends with a challenge, the result of which will be featured in a future podcast.

Let Chris, Craig, and Graeme know what you thought about the podcast by leaving a comment here on this post.

(Download File 31.8Mb, 26 min. 30 sec.)

The video mentioned near the end of the podcast is called Daft Hands. Here it is:

Photo Credit: Shadow singer by flickr user EugeniusD80

The Return of the Lost Scribe... whoops

So now we are well into exam review and for good reason. (There are only 6 classes left until the exam).

On Thursday our class consisted of five accumulation problems from the AP exams of five different years.

We completed them in groups and then Mr. K. went over them in class. The questions were not extremely hard, but there were a few tricky parts. I believe after Mr. K. discussed them in full, we understood where we had made our mistakes.

The more important part of the exercise was to notice how the same type of problem changed over the different years. Looking at them, you can see that the graphs are the most noticeable things that change. They become less familiar in behaviour and less points are actually drawn and labeled. The graphs also begin to have a lot of corners which are discrepancies in the second derivative as the are undefined. It then asks if these points are points of inflection, which are usually calculated via the second derivative. That is probably the trickiest part of these questions, but with a little understanding of how the derivatives and their graphs relate to each other, it is easy to get around.
The questions also change fairly drastically, as they go from just understanding how to use the graph and the given functions, to looking past the given graph and fuctions and using it to find characteristics of the parent/derivative functions and their graphs. In the later examples, they begin to ask questions about behaviour of the functions over certain intervals and even ask to draw the graph of the parent function on the axes.
The final example (from 2007) is quite different from the others as there is no graph given, but a table of values is. The table includes two functions (ƒ and g) and their derivatives. It then asks questions about the function h(x) = ƒ(g(x)) - 6 and how it behaves over certain intervals. It also asks a new question that we have not seen yet.
It asks us to find the derivative of the inverse of a function ( g^-1 ). It is a rule that Mr. K. has not yet taught us, but it was explained to me as "the derivative of an inverse of a function is equal to the inverse of its derivative" basically, ∂/∂x(g^-1) = 1/g'. From there just apply it as you would any derivative and solve the question.

Finally, Mr. K. said that this last example is probably the closest example of how it will be presented on our exam, so it would be a good idea to go over this some time in the next two weeks to make sure you have this under your belt, it should be easy marks now.

That is all for my scribe post, remember to start studying "fiendishly" (if you haven't already) there are only 18 days left. O_O

The next scribe is Van I guess...

Enjoy the rest of your weekends!

BOB

Woah! We had the test moved back two days and I still almost forgot.
But yes, this last unit has been okay mainly because it is just an elaboration on material we've already covered.
However, I believe the hardest part for me is that we started it quite a while ago. It's almost been a month since we began the unit.
But, it's nothing a little studying won't fix.
I'm trying to think of the parts that are most challenging, but none seem to stick out. I think the place where I'll make my mistakes is on the tricky little curves Mr. K. enjoys throwing into the tests =P
Anyway, this is the last unit and from now on it's all exam review.
It may seem like it's far away (a little less than a month), but there are ONLY 8 MORE CLASSES!!! So the intense studying should probably begin.... NOW!

Good Luck to all on the test tomorrow, and good luck to all on the upcoming exam.

Keep On Pushing!

HAPPY BIRTHDAY GRAEME!

HAPPY EIGHTEENTH BIRTHDAY!!!

***Craig-4th (belated)***
***Graeme-7th***
***Chris-13th (advanced)***

Much love ! =)
Good luck with your DEV =)


---Aichelle ROCKS!

Absolutely Late Scribe..... Sorry guys.

WOW! Very, very sorry about the tardiness of this scribe... I worked both last and this evening and today was very busy.

So Wednesday's class started with a very unusual period in which we were given our tests back and allowed 10 minutes to continue them since we didn't get a chance last Thursday.

Then we briefly discussed the Developing Expert Voices projects as Mr. K. handed back the proposals.

Following that was a little conversation about "π day" (which is today actually). I'm bringing either a Strawberry-Mango or Blueberry-Peach pie =D.

Finally we started the lesson for the day. The first thing we did was a quick review of Differential Problems.
It dealt with a set amount of oil in a reserve, states that a function A(t) as the rate of consumption, and provides the derivative of the rate [ A'(t) ]. How long until the reserve is completely emptied.

Basically, to solve it, find the antiderivative, A(t)+C, of the the given function and then plug in t=0 to find the constant (C).
From there it is as simple as finding the positive root of that function and that will be the answer.

Next we moved onto the new content.
SLOPE FIELDS

these are kind of tough to explain... I'll let some pictures speak some of my words.
This is the FIELD in which we plot the SLOPES. Easy enough right?
So we first tried it with the expression ( ∂y/∂x = y ). This means that the derivative of any point in the function is the value of the function at that point (y-coordinate).
•Let's say we want to plot the point (1,1). The derivative (SLOPE) of the function at that point is 1, so we draw a small line with slope 1 at that point.
•Next, take the point (3,2). The derivative at that point is 2, so there's another small line, but with a slope 2 at the point (3,2).
Now, you understand how they are constructed, this is how the SLOPE FIELD of the function(s) that have ( ∂y/∂x = y ).
From here, you can solve for the point (1,1).
To do this, draw a curve that follows the slope of the line in either direction until the next whole number is reached. At that point, change the curve's slope to that of the new poitn and continue until the next whole number and so on... WHAT FUNCTION DOES THE CURVE LOOK LIKE???
Correct! It is easy to see that the function that has a derivative equal to the value of the function and passes through the point (1,1) is y=e^x.
However, you can also see that there are many other functions with a similar shape that could have been drawn, depending on the starting point.
This is because the SLOPE FIELD shows the entire family of functions [ ∫ƒ(x)∂x + C ].
So, by solving for a point, you can find the exact one function from that family.

We also did SLOPE FIELDS for ∂y/∂x = 2x and ∂y/∂x = -x/y... can you guess what functions they are???















This was the end of the lesson as we realized that any function can be determined by plotting it's derivative in a SLOPE FIELD and we can find which function out of a family given a point on the specific function.


This concludes my scribe post, once again, sorry it was so late.

The scribe for PI (π) Day will be...

VAN!!!!!!!!!!

Craig's BOB

Well, just here to do a quick little B.O.B. The unit of Applications of Integrals has been a pretty interesting one because of how close it gets to real time problems. I have enjoyed solving these problems and even though at times they seemed complicated, once you leave all the words behind and put it into mathematical equations it became a lot easier.

As well, it gave a bit more practice for solving integrals a bit quicker and allowed us to use a lot of previous techniques/skills to do them.


I would have to say that the hardest part of the unit was the last bit with the radial density because of how much translation from real circumstances to mathematical equations and diagrams. However, once again as soon as it was translated, it became quite easy to solve.

So after the pre-test, we will see what kinds of questions to expect on the test, and what areas we need to brush up on a bit.


See you all tomorrow and good luck on the pre-test and test!

Post-Work Scribe...

Sorry to all, this scribe is very late due to the fact that I worked till 11 both nights and I just woke up from falling asleep at the computer... o_O

Okay, so Monday's class started for most people with walking into room 66 and getting ready to learn. Mine however started in the library as I was getting my Grad Pictures taken.

So, when I walked into class, a couple minutes had already gone by and Mr. K. was quickly going over the Exercises on Volumes of Revolution from Thursday's class. Now, over the weekend Grey-M did a pretty decent job posting the answers in his Scribe, but happened to make a couple of mistakes.

To make sure you don't make the same ones:
•RECOGNIZE THE DIFFERENCE BETWEEN VERTICAL AND HORIZONTAL FUNCTIONS (of "y" and of "x"), IDENTIFY WHICH TERMS THE INTEGRAL IS IN (x or y), AND REMEMBER THE DIRECTION OF REVOLUTION.

In depth corrections may be seen in the slides from today .

We then returned to the "Oil Leak Question" from Tuesday's class...

If you don't remember, the question was:
Now, to explain it briefly... the function given is in Gallons/Hour and the value we wish to obtain is in Gallons. So, you do the math... (we have to multiply by Hours). Now the amount of hours it takes to spill can also be represented as ∂t (change in time) which, when multiplied by the function, results in a neat looking integral which can then be solved from 0 to 10.

The next question we looked at was the "Density Question".
For this question, first visualize that there is a circular oil slick with a changing density (it is more dense in the center than it is towards the circumference). We are then told the density at any radius is given by a function. Once again looking at units, we see the function is in KG/m^2 and we need a value with units KG. So we need to multiply the function by the area of the slick and the area in terms of r is 2πr•∂r. So multiplying that onto the function once again provides an integral (thanks to the ∂r) and may be evaluated from 0 to 1000 to get the answer.

Part B of this question asks to find the smallest radius that contains 75% of the slick's mass.
So for this one, we take the integral to find mass used in the previous question and use "o to r" as the interval. As well, set it equal to 75% of the total mass (3255). By doing this, we have set the end of the interval as the variable and therefor the first value of "r" from 0 that equals 75% of the mass will be the result.
Once this is set up, integrate by parts with u=1+r^2 to solve it... the rest is grunt work =P



Then we moved on to a new question dealing with density of cars along a length of street.
This is very similar to the first question in terms of how we solve it. It says the function gives value with the units Number of Cars/KM and we need just the Number of Cars. So, we somehow need to multiply by KM. It says that x=KM so the distance from zero (∂x) can be multiplied by the function to once again CREATE AN INTEGRAL!!! (Surprise!)
To find how many cars are along a stretch of street of given length, just plug the length into the equation (x=length) and solve.




I believe that is all for this scribe... don't forget to do some homework!


Next Scribe is.........


ETHAN!!! Because I think he's the only one who hasn't done 7... I may be wrong, but yeah. You're scribe
XD

Anti-BOBing

Well yeeeeaah Craig is BOBing again. This unit has been quite interesting, I have enjoyed it thoroughly. It seems that this unit has pretty good for, most has just come natural (a good thing because of all the content I have missed due to sleeping... Sorry Mr. K!!!) But after this pre-test I fully understand the application of all the content of the unit. It has been a great unit with plenty of memorable classes (thanks to the SMARTBoard and computer being at its best) But, I should wrap up this Beee - Ohhh - Beee, because I have plenty of Physics to finish tonight...

Good Luck to all!!! =D

Keep On Pushing

-Craig

Last Minute BOB!!!

Oh my goodness! I was 20 minutes away from losing a mark on the test. Very sorry Mr. K., but I was focused on my World Issues project that was due today, so I forgot.

Anyway, this unit was a pretty good one, simply because it is a combination of a couple units we have learned previously. These last two weeks were pretty stressful for me, so I was not fully awake for some of the classes for this unit. There were points that I was quite unclear of, but thanks to Mr. K. and the rest of classmates, as well as the practice problems, I am pretty confident with the material.

If this is anything like the pre-test (I hope it is), this test should very fairly easy. However, Mr. K. always seems to throw in a question that throws me off, or maybe I just make simple mistakes.

In any event, I'm looking forward to seeing how I do on this test, AS WELL AS THE RESULTS OF THE LAST ONE =D...


Good luck, Keep pushing, see ya

BOB...

ARGH!!!! I still have to BOB!!!

Well here we go...

This unit was one that I liked because it really did not introduce many new topics at all. Even the derivative tests are just number lines (grades 11 and 12). So yes, that is why I didn't mind this unit.

My favorite part of it was the optimization problems... I particularly enjoy these because
I have always loved word problems, and I find they are very easy. I hope there are a couple on the test.

I believe
the toughest part for me is remembering to include the first/second derivative tests in my solutions for finding maximums and minimums. (Stupid mistakes, I hate them!)
I think that's about it... Good luck to all, and NOW I can finally get some sleep =)

KEEP PUSHING!!!

Pre-Test Scribe

Well well well, scribing again, it seems like it was only two weeks ago that I was scribing last... Oh wait, it was two weeks ago. =)

But today's class was a pre-test (YAY!)... this is awesome because it is going to be short and sweet and that is awesome because I had work tonight... GO FIGURE!

Anyway, yes we had a Pre-test, but before that Mr. K. briefly talked to us about what to expect for the rest of the year. Basically, coming up to the Winter Break and after that, there won't be too much pressure from Mr. K. because of other exams. However, once we get into April, the pressure is on!!! He will expect us to be doing practice questions from the AP exams in the Links section of the blog. As well, we have to have our question outlines for DEV in by next Monday.

With that we started our pre-test, it was not too tough (besides a couple mistakes), but not too easy either, like most of Mr. K.'s Pre-tests. Questions and answers/solutions may be seen here. Once again sorry this is so effortless, but work was tough and I need my sleep...

I think that the upcoming test will be quite difficult so make sure to study. BTW

REMEMBER:
USE THE FIRST OR SECOND DERIVATIVE TEST WHEN SOLVING FOR MAXIMUMS OR MINIMUMS (OPTIMIZATION PROBLEMS AS WELL)

That's about all for tonight... I guess I'll be scribing again soon (but hopefully not until after the break)

Next scribe is... ummm...

SANDY!!!


G'Night all!

Scribe #5 out of A LOT!

Today's amazing class started off with a bit of side-tracking. Mr. K. introduced us to a couple anecdotes that will be helpful to everyone in their overall learning skills. Now of course Mr. K. got them from a source that I am quite lazy enough not to discover... but they were:
LEVELS OF LEARNING (Bloom's Taxonomy)
Basically describes the different ways we can learn. They are Remember, Understand, Apply, Analyze, Evaluate, and Create. When we begin to learn in elementary, we start at the beginning and eventually climb up the levels of learning. Currently we are at the levels of Analyze and Evaluate, which still require all the others, and use them in class everyday.
LEARNING PYRAMID
Shows the different media (or methods) from which one can learn and the percentage of that knowledge that one would retain from each method. These methods are (in order):Lectures, Reading, Audio-Visual, Demonstrations, Discussions, Practicing by Doing, and Teaching. It turns out we only retain about 5% of knowledge from Lectures and a whopping 90% from teaching... that's a huge gap!
So in conclusion, Mr. K. told us that when we do our DEV (Developing Expert Voices projects)
, we are combining the Create and Teaching methods. That is one heck of a lot of learning that we do!!!

But now I will jump into the actual lesson of the day...

Well, we first did a quick review of the First Derivative Test, which is:
Next, Mr. K. introduced, the Second Derivative Test, which goes as follows:
We then jumped into some sample questions using this test. These can be seen on the slides for today's class. As well, you can click on the links underneath the definition of the tests on the green pages for more practice problems.


Next Mr. K. showed us a little loop-hole... It is thought that when the second derivative (ƒ''(x)) is equal to 0 (zero), there is a point of inflection on the parent function right??? The thing is, it might not be. It may in fact be only a candidate for the point of inflection. Then we must test the concavity on either side of this point (whether ƒ'' is positive or negative). If the concavity is different on each siide, it is a point of inflection, but if it is the same on both sides, the point is not a point of inflection, it is a local extreme that is relatively flat in a certain interval. AN EXAMPLE OF THIS IS THE FUNCTION ƒ(x)=x^4

We then continued with practice problems (which can be seen on the slides; link is above) until the end of class.

Quick thing to add to our understanding of these tests:

First Derivative Test: Interval test; find the candidates for global extrema and check the intervals on each side of them to prove they are in fact extrema.

Second Derivative Test: Point test; find candidates of global extrema and find the concavity of the parent function at each candidate.

Mr. K. has said, that one is not necessarily better than the other, they are just DIFFERENT... meaning in different situations, different tests will be better to use. (I like the Second one better)

That just about wraps up my Scribe for the evening...

REMEMBER GUYS: 5.2 ODDS FOR HOMEWORK!!!


Next Scribe is.......

BOB... I hope?

Yikes, based on the fact that I wasn't writing the test today, I forgot that we had to BOB before today... well ladies and gentlemen, this will be short and sweet. This has been quite an interesting unit to say the least. I have enjoyed it (except the pre-test) that was intense!!! But yeah I like doing the problems from this unit because it feels really good when you finally get the solution to the most complicated related rates problem!!! But really, nothing I'm too worried about, I'll study a lot... and I guess it's a little late for "Good Luck", but I guess "Let the Force Be With You" would be appropriate for the rest of the year... =)

Scribe Episode 4: The Return of the Jedi

Oh My Goodness!!! It is quite late, but the Scribe is finally up, I believe most of you will be reading this tomorrow, but that's okay, it will be a great review!!! And BTW, how late is it if it was posted before the slides were??? Haha, anyway, here it is... Please tell me if there's anything wrong =) (Oh DARN I already found one spelling mistake, please ignored the "shoed" in the second slide -_-

| View | Upload your own

BOO!!! It's my Halloween BOB

Hmmm... where to start, where to start...

Well, this unit has been fairly interesting because of its relation with the previous unit. Now I can begin to see how everything in Calculus ties together. I have enjoyed this unit quite a bit because it has a decent amount of material that relates to Physics...

As well, it is fairly straight forward with the math, not a lot of outside the box thinking...

A key thing to remember is:
- There is more than one way to find the integral of a function
1. Using the formula: lim(n-->∞) [ f(x1)•∂x1 + f(x2)•∂x2 + ... f(xn)•∂xn ]
2. The Riesum Program in our Calculators:
LEFT: (left side of the interval)
RIGHT:(right side of the interval)
X CHOICE: (0=Left Estimate)
(0.5=Midpoint Estimate)
(1=Right Estimate)
N: (number of sub intervals)
3. "fnInt" function in our calculators: fnInt(Y1, X, min, max)
4. the function "∫ ƒ(x)∂x" in the 2nd Trace (Calc.) Menu
5. Calculate it Manually: LEFT ESTIMATE: Sum of all "ƒ(x)"s, minus the last "ƒ(x)" then multiplied by ∂x.
RIGHT ESTIMATE: Sum of all "ƒ(x)"s, minus the first "ƒ(x)" then multiplied by ∂x.
TRAPEZOID SUM 1: Sum of the first "ƒ(x)", the last "ƒ(x)", and (2 • all the "ƒ(x)"s in between) Then multiplied by ∂x. Finally divide by 2.
TRAPEZOID SUM 2: (LEFT ESTIMATE + RIGHT ESTIMATE) /2

Well, that's pretty much all for my BOB, good luck tomorrow... and:

KEEP PUSHING, and maybe, just maybe, that rock will stay at the top...

Calculus BOB saluclaC

Well, BOBin' for the first time in Calculus... haha we got away with one last week.

Hmmm... well for anyone who thought Calculus should have been a little harder while doing the first unit, HERE YOU GO! Holy, honnestly, I did not expect it to be this big of a jump from the most familiar things to a brand new concept of Derivatives and Limits. WOW!!! Anyway, now I think I'm finally starting to get going with this stuff in the sense that I know EXACTLY WHAT I'M DOING!!! At the beginning of the unit, with two different teachers teaching, I found it a little difficult to stay on track. However, lately I've started to understand it a little more. One thing that I know I will probably have a little difficulty with is the limits portion... I never really knew exactly what was happening with them. Oh well, I'll see how they are in the review tonight. Other than that I think I should be set, although I'm sure I'll make a couple mistakes... nobody's perfect (cough*Chris*cough) LOL!!! just kidding....

Oh! Almost forgot! REMEMBER:

Keep pushing =)

The Scribe that didn't know he was the scribe until 3:33...

Haha, hmmm.... well to make a long story short, I looked at the blog briefly last night because I thought there was homework that needed to be posted (there wasn't) and while I was there, I completely forgot to check who the next scribe was. (evidently it was me). I learned from Aichelle a couple minutes after the end of class that I was, fortunately the class wasn't very complicated and no new concpets were really introduced. So, here we go with probably the easiest scribe post I've had to do in a while.

Well, this class was a "workshop" class, so we got into our groups and took a look at the first question which seemed very familiar. It has to do with the graph of the height of a thrown ball over time (Grade 11 Pre-Cal question). However he added the velocity of the ball which is the rate of change (a.k.a. derivative) of the function. Then we were asked a series of questions about the scenario. For question and answer, click the "first question link".
Question Two basically asked us to find the slopes of the tangent at each point and list them in increasing order.
The third question was a little interesting because it gave us a told us that an original function was transformed by with a vertical shift. Then it asked us about how the derivative of the transformed function related to that of the original function. Well, when a function is shifted vertically, the vertical and horizontal scale remains the same (same size), as does the shape and it's position along the x-axis (x coordinates). The only thing that differs between it and it's original function is the y coordinates. Now, we know that a derivative is a graph of the slope of the tangents of the parent function vs. the points along the x-axis. So, since the shape, size, and x coordinates of the transformed function do not change, the slope of tangent at each point remain the same meaning the derivatives are the same!!!.
When Mr. K. clicked the next slide button on the SmartBoard Question Four came on the screen. This dealt with the derivatives of even and odd functions. Basically, the derivative of a point [ie. (4,2)] on a even function will result in a derivative that is equal, but opposite at the point that is opposite about the y-axis [(-4,2)]. When dealing with an odd function, the derivative at one point [ie. (1,3)] will be the exact same as the derivative of the point opposite about the origin [(-4,-2)].
Finally, we finished with two questions that were connected. Question Five was the last one we worked with, but has the same rule as Question Six which is to be completed and posted in the comments box this evening. For an explanation of how to do these two, click here.

Well, that concludes my scribe post for the night. I shall post my answer to the Homework question in the comment box now that at least some people have tried to answer it.
Don't Forget:
-PRETEST TOMORROW!!!
-TEST ON FRIDAY!!!
-B.O.B. BEFORE THE TEST (excluding Aichelle as she has already done so)

LAST BUT NOT LEAST, THE NEXT SCRIBE WILL BEEEEEEE:

...

...

...

once again I pick GREY M!!!

good night =D

BTW Mr. K. I am not feeling too amazing at the moment, so I'm not entirely sure if I'll be at school tomorrow.

"A Scribe of Excellence"

WOW!!! Very sorry for the lateness of this scribe. I have just returned from "An Evening of Excellence" (for those who don't know: our school's awards ceremony) at which, I must add, our Calculus class did quite exceptionally. =D Now here I go with my Scribelicious post:

As we all took our seats in class today, we were presented with a picture of waves, which could only mean one thing: TRIGONOMETRY. It was in fact a review of the stuff we had learned in our previous years.
The first thing that we were told to do is take a look at the page on the Weather Network's web page, choose a statistic and find a periodic (sinusoidal) function that would fit the data. Of course we used our calculators, so this wasn't too difficult. We found that the two best fits for a sinusoidal function were MAXIMUM TEMPERATURE and SUNSHINE.
Next, we entered the real review part of the lesson; we were given a graph of a sinusoidal function and were told to write two equations for it. (see questions and answers here.)
Now there are two formulae that may be used to write an equation:

f(x)=Asin[B(x-C)]+D and f(x)=Asin(Bx-BC)+D

The first is the easier one to derive from a graph and it is the way it was originally taught to most of us. The other is there because it is possible that you might see functions written either way on an exam or test.
The parameters of these formulae are as follows (just a refresher):

A = AMPLITUDE(vertical stretch)
B = PERIOD STRETCH(determines the Period via 2π/B)
C = PERIOD SHIFT(horizontal shift)
D = SINUSOIDAL AXIS(vertical shift)

***REMEMBER: when using your calculator to find an equation(STAT, SinReg), it will appear as f(x)=Asin(Bx+C)+D. The B has not yet been factored out, and C is being added, not subtracted. Therefore, to find the value of C, divide by -B!!!***
After that quick review, we received a question that gave us an equation of a function and told us to graph them...
So, when graphing these functions, take a look at the given functions and compare them to the ones above. The next step is to figure out the value of each parameter make sure B is factored outside the brackets!!! Then just follow these easy steps:
1. Using the AMPLITUDE and SINUSOIDAL AXIS, determine the max. and min. of the graph. Then scale y-axis accordingly. Draw a dotted line for the Sinusoidal Axis.
2. Using p=2π/B, determine the period of the graph and scale the x-axis from -P to P unless otherwise instructed. Scale the axis with a mark on each quarter of the period.
3. Draw dots (outline) using the PERIOD SHIFT to determine the starting x-coordinate on the Sinusoidal Axis. The starting position depends on which trigonometric function is being used and the sign of the AMPLITUDE.
4. Finally draw a smooth, fluid curve that connects each point. NO SHARP CORNERS OR EDGES!!!.
Next Mr. K. flipped quickly to a review on the Trigonometric Identities, but did not have much time to go over it. Maybe we'll go over it in class, but just in case, take a quick look at it on SLIDE 6. He also announced that we will be having a quick MENTAL MATH quiz on the values of the Unit Circle... make sure to look over that before you go to bed tonight.

The HOMEWORK for tonight is: Exercise 1.10 Questions #1,2,3,5,6,13.

NEXT SCRIBE IS:

----------------
Now playing: Linkin Park - Shadow Of The Day
via FoxyTunes

Late Scribe... But I did say it would be.

Well, well, well. Where to start? i guess the beginning of class would be a good place, if I can remember it... (please bear with me, I'm a little worn out)

So however it started, it did. Mr. K. introduced the day's topic as Exponential Modeling. We began this familiar unit by adding the new stuff that we had learned yesterday to it.SLIDE2 We were told to use our new TI-83 skills to plot the data, and then graph an exponential curve that relates to the data. We were kind of confused with this considering the scatter plot curve didn't resemble the exponential one very well. It was then that Mr. K. explained that when using "REAL DATA" (as we were), the graph may seem less accurate and straight forward as simulated data. this is because REAL DATA must deal with unexpected factors that interrupts the pattern (war, disease, etc.). Shortly after that, he began to see if we had retained any idea of the concept in our brains over the summer. For some very tired students (me), it took a little while, but we (I) got it nonetheless. When given the next example and told to write the equation for the function, we used the formula:

A=A(naught)(model)^t/p

Where...
A= final amount (amount present after t has passed)
A(naught)=the original or present amount
model=the percent growth expressed as a decimal +1
t = time (time needed to reach A)
p = period (amount of time between each application of the model)

Using this formula we constructed a model for the price of a BigMac in Canada in the future (Slide3). This was a really cool question, the study was really original. If you want to have a look at it, click here.

Next, Mr. K. took a little detour and talked a little bit about how the value of currency can change. He used the fact that the German mark, from the time it was offered as a reward for Fermat's last proof to the present day, has decreased in value so massively that 100 000 then is probably worth about 5 cents now.

Finally, we continued our "memory re-jogging" with one final question about the half-lives of chemicals (Slide5).

T'was around time that Mr. K. was putting the finishing touches on the solutions that the bell rang. Before we left, he added that Exercise 1.4: Odd Questions + 6, 12, and 14. were for HOMEWORK!!!

So before you leave this post, I will add that Vincent, no... John D, no... Jojo? no...

...hmmm who is left in this class???

Oh I know! Robert P is the scribe for tomorrow!!! =P

Good night! =D


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