Question

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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?

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13 hours 2021-10-12T13:28:51+00:00 1 Answer 0

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