ANSWER ASAP PLS!!!!! A scientist is studying the growth of a particular species of plant. He writes the following equation to sh

Question

ANSWER ASAP PLS!!!!!

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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Gia Bảo 4 years 2021-08-15T23:24:06+00:00 1 Answers 339 views 0

Answers ( )

  1. Philomena
    1
    2021-08-15T23:25:17+00:00
    Reply

    Answer:

    see below

    Step-by-step explanation:

    f(n) = 10(1.02)^n

    Part A

    Let f(n) = 11.04

    11.04 = 10 * 1.02 ^n

    Divide each side by 10

    11.04/10 = 1.02^n

    1.104 = 1.02^n

    Taking the log of each side

    log 1.104 = log 1.02^n

    We know log a^b = b log a

    log 1.104 = n log 1.02

    log 1.104 / log 1.02 = n

    4.99630=n

    Rounding n to 5

    The domain should be 0 ≤n≤5

    Part B

    f(n) = 10(1.02)^n

    The function is in the form y =a b^x  where a is the y intercept

    The y intercept is 10.  This is the value when n =0 days.

    Part C

    To find the average rate of change

    f(5) – f(1)

    ———–

    5-1

    f(5) = 11.04  

    f(1) = 10 *1.02 =10.2

    11.04 – 10.2

    ———–

    5-1

    .84

    —–

    4

    .21 cm per day

    The average rate of growth over the 4 days is .21 cm per day

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