Tuesday, September 18, 2007

Exponential Functions Lab

I'll do this by writing out the lab questions and putting the answers beside the questions.

Introduction: In this assignment you will explore what you can recall about exponential functions.

Background: Definition Let a be a positive real number. The exponential function with base a is the function: f(x) = a^x

- The domain of f(x) = a^x consists of all real numbers
- The range of f(x) = a^x is the collection of all positve real numbers
- If a<1 color="#ff0000">a>1 then f is an increasing function.
- Exponential functions satisfy the following properties:

1. a^r x a^s = a^(r+s)
2. a r/as = a^(r-s)
3. (a^r)^s = a^rs
4. a^r x b^r = (ab)^r

Investigation:

1. How is a linear function similar to an expoential function? How is a linear function different than an exponential function?

Similarities:

input and an output
variables
rate of growth

Differences:

no slope (changing slope)
no common differences, but a common ratio
arithmetic and geometric

2. Let f be the exponential function f(x) = 3 x 4^x. What is the y-intercept? What is the growth factor?

y-int: y = 3
3-> 12 -> 48

Common ratio = 4

3. Let f(x) = a^x such that f(1) = 6 What is the value of a? How do you know?

f(x) = a^x f(1) = 6
6 = a^1 therefore a = 6

4. Let f(x) = a^x. In the following graph of f, is a greater than one or less than one? How do you know?

f(x) = a^x
Since it's always decreasing, a must be multiplying each interval by a value less than 1.

5. Give the equation for the exponential function whose y-intercept is 2 and whose growth factor is 5.

f(x) = 2 x 5^x

6. Some chicken left on the kitchen counter has salmonella bacteria growing on it. The bacteria doubles every 6 hours. Explain why this is equivalent to a sixteen fold increase each day?

Four times in one day it would double, so 2^4 would be how much the bacteria increased, which is the number of bacteria per day, x 16.

"That's it, that's all, it's been a pleasure having you, go out there and commit random acts of kindness and have yourself a holly jolly great day." <-- Mr. K

I think that's how it goes... I'm not entirely sure >_>'

Group: Dino, Chris, Timmy, Van

Sorry if a I spelled your name wrong Dino. (Deno?)

7 comments:

aichelle s. said...

I like how you posted up all the questions. I agree with all your answers except for question 6...you put 2^4 I think you mixed that up and it should be 4^2. Your group also had more points in question 1 than we did. Good stuff though!

aichelle s. said...

Oh wait I see what you did nevermind disregard that last thing I said, sorry.

aichelle s. said...

By last thing I mean question six..lol..sorry about that.

m@rk said...

good job guys!!!
well, we came up with similar solutions from you guys . However, there are some minor differences on our answers in question 1 .
In question 1, we added some extra points on their similarities like they both have infinite ranges with the exception of horizontal lines, their domain is infinite,they are used to model real life situations,and both have y-intercepts. In addition to that, we also have some extra points on their differences like in order to find a slope of a exponential graph we use tangent lines .Other than that we mentioned the same things.

Robert P said...

We all have the basic idea now. I strongly agree with your answers to all guestions and took a look at your answers for question one which differed from ours. Good job guys!

Grey-M said...

Everything looks good... All the answers between our groups seem to correspond.

Phuong said...

Great job guys. It looks like everyone in the class seems to be on the same page. (: