Question

HELP ASAP 100PTS PART A AND PART B

DONT COPY OTHERS I CAN TELL AND REPORT YOU



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?

Answer 1

"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

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"quoted from

"calculista"

Answer 2

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

Part B) The average rate of change is
`0.21\ (cm)/(day)`

see the explanation

Explanation:

Part A)

Let

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

n ----> the number of days

we have

`f(n)=10(1.02)^n`

This is a exponential function of the form

`f(x)=a(b)^x`

where

a is the initial value

b is the base

r is the rate of growth

b=(1+r)

In this problem we have

`a=10\ cm` ----> initial value or y-intercept

`b=1.02\\r=b-1=1.02-1=0.02\\r=2\%`

For f(n)=11.04 cm

Find the value of n

substitute in the exponential function

`11.04=10(1.02)^n\\11.04/10=(1.02)^n\\1.104=(1.02)^n`

Apply log both sides

`log(1.104)=(n)log(1.02)\\n=log(1.104)/log(1.02)\\n=5\ days`

so

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

`0 \leq x \leq 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

`(f(b)-f(a))/(b-a)`

In this problem we have

`f(a)=f(1)=10(1.02)^1=10.2\ cm  f(b)=f(5)=10(1.02)^5=11.04\ cm\\a=1\\b=5\\`

Substitute

`(11.04-10.2)/(5-1)=0.21\ (cm)/(day)`

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