September 14, 2006

Exponential Functions Lab

Group members: Lindsay, Christian, Jann, Suzanne.

Similarities: If either a linear or exponential function is increasing or decreasing, they do so across the entire domain. Neither will begin as an increasing function and suddenly begin to decrease.

Differences:

a) In a linear equation, for every equal change in input, there is an equal change in output (in other words, a line has a constant slope). The outputs of an exponential function do not change at the same rate, but instead increase by a factor of x.

b) The highest exponent in a linear function is 1.

c) Exponential functions have an asymptote at y = 0.

d) Exponential functions always pass through the point (0,1), while linear functions don’t have to.

2. a) f(x) = 3∙4^x
f(0) = 3∙4^0
f(0) = 3

b) This function has a growth factor of 4.

3. f(x) = a^x
f(1) = a^1 , f(1) = 6

therefore:
a^1 = 6
a = 6

4. The function in the graph is decreasing, therefore a<1 according to the background information provided for the lab.

5. f(x) = 2∙5^x

6. The bacteria doubles every six hours, which amounts to a total of 4 times per day. So the number of bacteria is increased by 2^4, or 16, times per day. This exponential function can be described using the equation f(x)= b ∙ 2^x, where b is the initial # of bacteria, and time per 6 hours is x.

Sorry this is being posted rather late, guys. Oh, and Lindsay says:
varsity girls have a tournament friday and saturday, home court..... support marooonnnns!

13 comments:

ashlynn said...

I thought that your answers were very helpful and clear. It made sense. Your answers were very thorough and well done.

linger said...

I think you guys made really good points in stating the similarities and differences, and yes linear functions DO have exponents to the power of 1. Nicely done guys =D

katrin said...

You guys provided answers that were all very well said and very well explained. With that said, it helped me understand exponential functions more. That made me happy =] Great job!

christian said...

I think this group made a wonderful job in explaining the questions and answers. Perhaps colour would work too? or graphics? Just a couple of suggestions.

Anh said...

Like linger, I also think your group makes very good points on simmilarities and differences of linear and exponential functions.
Your points make complete sense and are easy to understand. Good job. =)

danny said...

They all look great an I understood them all, so job well done guys

charlotte said...

Wow, u gys have an awesome group. Wat can u ask for, all of u are
S-M-a-R-t. WEll u gys covered and answered all the question and it was done Nicely! I followed u throug till the end. As Christian said, it would have been a lot nicer if u add some graphs or colours, but other than that u gys did a wonderful job!

Manny said...

Very well done. The solutions are simple and clear, and well organized with usuage of spacing.

The only thing I suggest you add is at the last problem. The value of b is equal to 1, so your equation would look like f(x) = 2^x
instead of f(x) = b * 2^x.

And go maroons!

M-A-R-K said...

i agree with your answers, as some are the same as ours. Your group had a different asnwer for number one, but that answer works our. It was different and made sense. The only answer i'm not sure is correct for your group is number six. I just suggest that you should space out number six. It's all too close together.

loso said...

Great work you guys. Your answers are clear, well thought out, and a head noddeer. Each group pointed out some great facts with the first question; all with similarities and differences. I think that's a strong point for everyone, and a great thing to work with. Kudos!

char__lene said...

you guys eplained your answers throughly and even used all the mathematical terms. you guys made things more clear for me. but i did notice that you guys never mentioned that exponential functions decrease too. overall you guys did an Awesome Job.

crystal said...

Awesome job guys! There's great use of mathematical terms, especially in question 1. Sometimes I get used to describing them vaguely and forget about the correct terminology. Then when I look back on my notes I have no clue what I'm talking about. So this helped me describe them better, which would be helpful on tests and exams. Also, you can never go wrong with graphs and color.

Lani said...

Hi all,

I stayed on the side during this conversation because it was yours! What a joy to view a talented group of young people work collaboratively to achieve such a level of learning! Learning really is conversation, don’t you think?


Best,
Lani