can someone answer pleaseeee A scientist is studying the growth of a particular species of plant. He writes the following

Question

can someone answer pleaseeee

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? (4 points)

Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)

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? (4 points)

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Thái Dương 1 month 2021-08-15T21:37:51+00:00 1 Answers 1 views 0

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    2021-08-15T21:39:16+00:00

    Answer:

    Step-by-step explanation:

    11.04 = 10(1.02)^n

    1.104 = 1.02^n

    ln 1.104 = ln 1.02^n

    ln 1.104 = n ln 1.02

    n = ln 1.104/ ln 1.02

    n = 4.99630409516

    4.99 can be rounded to 5.

    So a reasonable domain would be 0 ≤ x < 5

    PART B)

    f(0) = 10(1.02)^0

    f(0) = 10(1)

    f(0) = 10

    The y-intercept represents the height of the plant when they began the experiment.

    f(1) = 10(1.02)^1

    f(1) = 10(1.02)

    f(1) = 10.2

    (1, 10.2)


    f(5) = 10(1.02)^5

    f(5) = 10(1.1040808)

    f(5) = 11.040808

    f(1)=10(1.02)^1

    f(1)=10.2

    Average rate= (fn2-fn1)/(n2-n1)

                         =11.04-10.2/(5-1)

                        =0.22

    the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.  

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