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) = 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?

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 = 3 to n = 10, and what does it represent?

Part A) A reasonable domain is the interval [0,10]  

Part B) The y-intercept is the height of the plant at the begin of the scientist study (initial height of the plant)

Part C) The average rate of change is  (see the explanation)

Step-by-step explanation:

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?

we have

where

n is the number of days

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

For f(n)=16.13 cm

substitute

solve for n

Apply log both sides

therefore

A reasonable domain is the interval [0,10]

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

we have

The y-intercept is the value of y when the value of x is equal to zero

In this context the y-intercept is the height of the plant at the begin of the scientist study (initial height of the plant)

For n=0

-----> initial height of the plant

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?

we know that

To find the average rate of change, we divide the change in the output value by the change in the input value

In this problem we have

Substitute

it tells us that the plant on average grows 0.43 cm each day, between day 3 and day 10

no

step-by-step explanation: