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?

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?

Answer 1

@paki

Answer 2

Hey Lexis :)
So we're given a growth function which corresponds to height: \(\Large\rm f(n)=8(1.05)^n\)
And we're told that the final height is 11.26.\[\Large\rm 11.26=8(1.05)^n\]

Answer 3

Your domain is the restrictions we put on the number of days.
We don't want our domain to be something like 0 to infinity, we can't have an infinite number of days, that would be silly.

Answer 4

We need it to apply appropriately to this problem.
So clearly, we'll start counting from day 0.
But where do we end?
Well we have the height at the final day, we can solve that equation for n to figure out how long the study lasted.

Answer 5

\[\Large\rm 11.26=8(1.05)^n\]We'll have to take the log of each side to get the n out of the exponent,\[\Large\rm \log11.26=\log(8(1.05)^n)\]And now we have to apply some log rules I guess.

Answer 6

Using our Log Product Rule,\[\Large\rm \log(11.26)=\log(8)+\log((1.05)^n)\]And then using our Log Power Rule,\[\Large\rm \log(11.26)=\log(8)+n\log(1.05)\]

Answer 7

Good! So we've gotten the n OUT of the exponent position.
Now you can solve for n by moving some stuff around.

Answer 8

@zepdrix OK I NEED HELP ON MORE