Asap 100pts part a and part b
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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) = 10(1.02)n

part a: when the scientist concluded his study, the height of the plant was approximately 11.04 cm. what is a reasonable domain to plot the growth function?

part b: what is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent?

Part A) The reasonable domain to plot  the growth function is the interval [0,5]

Part B) The average rate of change is

see the explanation

Step-by-step explanation:

Part A)

Let

f(n) -----> the height of the plant in cm

n ----> the number of days

we have

This is a exponential function of the form

where

a is the initial value

b is the base

r is the rate of growth

b=(1+r)

In this problem we have

----> initial value or y-intercept

For f(n)=11.04 cm

Find the value of n

substitute in the exponential function

Apply log both sides

so

The reasonable domain to plot  the growth function is the interval -----> [0,5]

Part B) What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent?

the average rate of change is equal to

In this problem we have

Substitute

The average rate of change is the change of the function values (output values) divided by the change of the input values.

That represent ----> The plant grew an average of 0.21 cm per day during that time interval

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