Question

Gotta repost this! EDITED: PLEASE HELP WITH PART C

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?

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

Here is my answer for A:

(Domain ≥ n > because it means time.) Domain value of n, solve for g(n) = 11.26 we get 7.005 reasonable range to plot the graph would be from n = 0 to 8.

Answer 2

that's right! the requested domain is given by the subsequent set:
\[D = \left\{ {n \in \mathbb{N}\;{\text{such}}\;{\text{that}}\;0 \leqslant n \leqslant 8} \right\}\]

Answer 3

@Michele_Laino great thank you! I have B & C can you check those also?

Answer 4

hint:
part B
the \(y-\)intercept, is the value of the function \(f(n)\) at \(n=0\)
so, what can you conclude?

Answer 5

\(n=0\) means the first day or day=0

Answer 6

The y intercept is the point where n = 0.. but n represents the number of days. (the y intercept is the plants initial height at n = 0) this is what I have

Answer 7

that's right! \(f(0)\) represents the height at initial day of experimental observation

Answer 8

part C
hint:
here the requested average rate \(r\), is given by the subsequent formula:
\[r = \frac{{f\left( 6 \right) - f\left( 2 \right)}}{{6 - 2}}\]

Answer 9

here is the next step:
\[\Large r = \frac{{f\left( 6 \right) - f\left( 2 \right)}}{{6 - 2}} = \frac{{8 \cdot {{1.05}^6} - 8 \cdot {{1.05}^2}}}{4} = ...?\]

Answer 10

average growth rate from n = 2 to n = 6 is found by establishing in height and diving the length of passing time. The constant rate of change is 8.4.

Answer 11

please note that the question asks for an average value, not a constant value, am I right?

Answer 12

@Michele_Laino oh you're right

Answer 13

here is another step:
\[\Large \begin{gathered}
r = \frac{{f\left( 6 \right) - f\left( 2 \right)}}{{6 - 2}} = \frac{{8 \cdot {{1.05}^6} - 8 \cdot {{1.05}^2}}}{4} = \hfill \\
\hfill \\
= \frac{8}{4} \cdot \left( {{{1.05}^6} - {{1.05}^2}} \right) = ...? \hfill \\
\end{gathered} \]

Answer 14

ermm well 8/4 * (1.05^6 - 1.05^2) = 0.475191 right?

Answer 15

yes thats correct :)

Answer 16

@bubblegum. ah okay.. wait then what would part C be?

Answer 17

@Michele_Laino can you help me with part C?

Answer 18

part C
average rate is \(r=0.475\), as computed before

Answer 19

it represents, the increasing of the height of the plant over time, as the number of days increases from 2 to 6

Answer 20

@Michele_Laino thank you so much!

Answer 21

:)