PLEASE HELP 100PTS!!!!!!!! I SOLVED IT BUT I WANT TO CHECK MY ANSWERS!! DONT COPY OTHER ANSWERS I CAN TELL AND REPORT YOU!!!!

Question

PLEASE HELP 100PTS!!!!!!!! I SOLVED IT BUT I WANT TO CHECK MY ANSWERS!!

DONT COPY OTHER ANSWERS 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?

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

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    2021-10-12T13:29:52+00:00

    Answer:

    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\ \frac{cm}{day}

    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

    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

    \frac{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

    \frac{11.04-10.2}{5-1}=0.21\ \frac{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

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