Ascientist 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 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 = 1 to n = 5, and what does it represent?

Part A) The reasonable domain for n is the interval  [0,5]

Part B) The y-intercept is the height of the plant at the beginning of the study

Part C) The average rate of change is

Step-by-step explanation:

Part A)

we have

This is a exponential function of the form

where

f(n) is the height of the plant in cm

n is the number of days

a is the initial value or y-intercept of the function

b is the base

r is the rate of growth

b=(1+r)

In this problem we have

----> initial value or y-intercept (value of he function when the value of n is equal to zero)

For f(n)=11.04 cm ----> Find the value of n

Apply log both sides

Solve for n

therefore

The reasonable domain for n is the interval  [0,5]

Part B) What does the y-intercept of the graph of the function f(n) represent?

we know that

The y-intercept or initial value of the function is equal to 10 cm

Remember that the y-intercept is the value of the function f(n) when the value of n is equal to zero

so

In this context the y-intercept is the height of the plant at the beginning of the study

Part C) 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

the answer is c. 23/3