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) = 12(1.03)n

Part A: When the scientist concluded his study, the height of the plant was approximately 16.13 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 = 3 to n = 10, and what does it represent? (4 points)

Answer 1

n is an exponent, right?

Answer 2

yah

Answer 3

You mean this function:

\(\large f(n) = 12(1.03)^n\)

Answer 4

Set the function equal to 16.3 and solve for n.
That will give you an idea of the domain you need for n.

Answer 5

how do I do that?

Answer 6

You need to use logs to solve for an exponent.

Answer 7

idkhow

Answer 8

Here is an example:

\(24 = 4(5.5)^x\)

First, switch sides to have the variable on the left side.

\(4(5.5)^x = 24\)

Divide both sides by 4

\(\dfrac{4(5.5)^x}{4} =\dfrac{24}{4}\)

\((5.5)^x=6\)

Take log of both sides

\(\log (5.5)^x = \log 6\)]

The log of an exponent is a multiplier

\(x \log 5.5 = \log 6\)

Divide both sides by \(\log 5.5\)

\(x = \dfrac{\log 6}{\log 5.5} \)

\(x \approx \dfrac{0.77815}{0.74036}\)

\(x \approx 1.0510\)