Monday, September 17, 2007

Exponential Functions Lab: Team Sandy/Robert/Aichelle

Our group consisted of Sandy, Robert and me, Aichelle.

For question one, we came up with:
similar---> both have inverses.
different---> linear functions have a common difference; exponential functions have a common ratio.

For question two, we said the y-int. was 3 and the growth factor was 4.

We found the value of a to be six in question three.
We know this because:
we were given: f(x) = a ^ x and f(1)=6
so that means a ^ x = 6
and if x = 1
then, a ^ x = a ^ 1
a ^ 1 = 6
a ^ 1= 6 ^ 1
since they have the same exponent [1] we can say a = 6.

We said the graph is less than one because the graph is decreasing. As the x-value increases, the y-value decreases. Therefore, a has to be less than 1 in order for that to occur.

For question five we came up with an equation of f(x) = 2 * 5 ^ x.

And lastly, for question 6, we said that the salmonella bacteria growth that doubles every six hours is equivalent to a sixteen fold increase each day because:
there are 24 hours in a day and it takes 6 hours for the bacteria to double.
24hrs/6 hrs = 4 times the bacteria doubles in a day.
since it is doubling we must square how many times in doubles in a day.
4² = 16 times or 16 folds in a day.



Tim_MATH_y said...

Well done group! In our group, we came up with identical solutions; however, our answers to question number one differed in the way that we had different points.

We did not state that both linear and exponential functions have inverses, that was a great one.

Some similarities we included were that they all included a rate of growth and included variables (input/outputs, independent and dependent variables).

Differences that we included were that linear functions followed a common difference and were arithmetic whereas exponential functions followed a common ratio and were geometric.

aichelle s. said...

oh that's more than what we came up with and the points your group made are great.

m@rk said...

good job everyone!!!
well, we came up with similar solutions from you guys so i think it is true that "bright minds think alike". However, there are some minor differences on our answers in question 1 and 6.
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 and they are used to model real life situations. In addition to that, we also have some extra points on their differences like a linear function has a constant slope and that we use tangent lines in finding the slope of an exponential function.
In question 6, we have different explanations on how 16 folds is similar to the growth of the salmonella bacteria.

MrSiwWy said...

Good job group! Our answers are the same, though explanations might differ slightly. Also, you did not have as many points in the contrast portion, though the points present were extremely good points.

Differeneces that you could have included refer to the arithmetic quality of linear functions, as well as the geometric quality connected to exponential functions. Also, you could have included (my group as well) values or intervals that each may reside within or pertain to or not, such as y-intercepts or asymptotes,etc.

Overall, good job on the assignment, and I like how simplistic and usually blatantly obvious qualities of functions (as found within each groups comparisons) are somtimes overlooked, such as the fact that both linear and exponential functions have inverses as stated by your group.

Grey-M said...

A job well done. All the answers look good. Couple more points could have been added to the similarities and differences but that's been covered by others...