celinegirl
  • celinegirl
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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celinegirl
  • celinegirl
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.
Michele_Laino
  • Michele_Laino
that's right! the requested domain is given by the subsequent set: \[D = \left\{ {n \in \mathbb{N}\;{\text{such}}\;{\text{that}}\;0 \leqslant n \leqslant 8} \right\}\]
celinegirl
  • celinegirl
@Michele_Laino great thank you! I have B & C can you check those also?

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Michele_Laino
  • Michele_Laino
hint: part B the \(y-\)intercept, is the value of the function \(f(n)\) at \(n=0\) so, what can you conclude?
Michele_Laino
  • Michele_Laino
\(n=0\) means the first day or day=0
celinegirl
  • celinegirl
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
Michele_Laino
  • Michele_Laino
that's right! \(f(0)\) represents the height at initial day of experimental observation
Michele_Laino
  • Michele_Laino
part C hint: here the requested average rate \(r\), is given by the subsequent formula: \[r = \frac{{f\left( 6 \right) - f\left( 2 \right)}}{{6 - 2}}\]
Michele_Laino
  • Michele_Laino
here is the next step: \[\Large r = \frac{{f\left( 6 \right) - f\left( 2 \right)}}{{6 - 2}} = \frac{{8 \cdot {{1.05}^6} - 8 \cdot {{1.05}^2}}}{4} = ...?\]
celinegirl
  • celinegirl
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.
Michele_Laino
  • Michele_Laino
please note that the question asks for an average value, not a constant value, am I right?
celinegirl
  • celinegirl
@Michele_Laino oh you're right
Michele_Laino
  • Michele_Laino
here is another step: \[\Large \begin{gathered} r = \frac{{f\left( 6 \right) - f\left( 2 \right)}}{{6 - 2}} = \frac{{8 \cdot {{1.05}^6} - 8 \cdot {{1.05}^2}}}{4} = \hfill \\ \hfill \\ = \frac{8}{4} \cdot \left( {{{1.05}^6} - {{1.05}^2}} \right) = ...? \hfill \\ \end{gathered} \]
celinegirl
  • celinegirl
ermm well 8/4 * (1.05^6 - 1.05^2) = 0.475191 right?
bubblegum.
  • bubblegum.
yes thats correct :)
celinegirl
  • celinegirl
@bubblegum. ah okay.. wait then what would part C be?
celinegirl
  • celinegirl
@Michele_Laino can you help me with part C?
Michele_Laino
  • Michele_Laino
part C average rate is \(r=0.475\), as computed before
Michele_Laino
  • Michele_Laino
it represents, the increasing of the height of the plant over time, as the number of days increases from 2 to 6
celinegirl
  • celinegirl
@Michele_Laino thank you so much!
Michele_Laino
  • Michele_Laino
:)

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