Question

A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:

f(n) = 8(1.05)n

Part A: When the scientist concluded his study, the height of the plant was approximately 11.26 cm. What is a reasonable domain to plot the growth function? (4 points)

Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)

Part C: What is the average rate of change of the function f(n) from n = 2 to n = 6, and what does it represent? (4 points)

Answer 1

@dan815

Answer 2

@PeterPan

Answer 3

\[f(n) = 8(1.05)^n \] When the scientist concluded his study, the height of the plant was approximately 11.26 cm. What is a reasonable domain to plot the growth function?

\[11.26=8\times (1.05)^n\] solve for \(n\)

Answer 4

3?

Answer 5

i dunno i didn't do it
hold on and i can check

Answer 6

no

Answer 7

Ok

Answer 8

divide by 8, use the change of base formula and a calculator
of course since you have to use a calculator anyways you might as well cut to the chase
http://www.wolframalpha.com/input/?i=11.26%3D8%281.05%29^x

Answer 9

ok

Answer 10

so it would be 7?

Answer 11

that is what the wolf says, yes
wolf is very smart so i would not argue

Answer 12

ok lol

Answer 13

that would put the domain at \(0\leq n\leq 7\)

Answer 14

ok

Answer 15

What does the y-intercept of the graph of the function f(n) represent?

what is what you get if \(n=0\) which is how high it was at the beginning, when he started counting

Answer 16

it is the number out front since \(b^0=1\) always

Answer 17

Yes

Answer 18

What is the average rate of change of the function f(n) from n = 2 to n = 6,

\[\frac{f(6)-f(2)}{6-2}\] whatever that is

Answer 19

and what does it represent? (4 points)

it represents... the average rate of change! (doh)

Answer 20

yess

Answer 21

Can you help with part b @satellite73