Jill has been watching the squirrels that live in her neighborhood. The number of squirrels changes each week. n f(n)

Question

Jill has been watching the squirrels that live in her neighborhood. The number of squirrels changes each week.

n f(n)
1 8
2 12
3 18
4 27

Which function best shows the relationship between n and f(n)?
f(n) = 12(1.5)n
f(n) = 12(1.5)n−1
f(n) = 8(1.5)n
f(n) = 8(1.5)n−1

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Liliana 2 weeks 2021-09-10T08:37:23+00:00 2 Answers 0

Answers ( )

    0
    2021-09-10T08:38:40+00:00

    Answer:

    The answer is D

    Step-by-step explanation:

    0
    2021-09-10T08:39:02+00:00

    Option D: f(n)=8(1.5)^{n-1} is the function that represents the relationship between n and f(n)

    Explanation:

    Let n represents the weeks

    Let f(n) represents the number of squirrels.

    We need to determine the function that represents the relationship between n and f(n)

    The given sequence is a geometric sequence.

    First, we shall determine the common difference.

    r=\frac{12}{8} =1.5

    r=\frac{18}{12} =1.5

    r=\frac{27}{18} =1.5

    Thus, the common difference are equal.

    The equation of the function can be determined using the formula,

    a(n)=a(r)^{n-1}

    where a is the first term and r is the common difference.

    Substituting the values, we have,

    a(n)=8(1.5)^{n-1}

    Hence, the function is given by

    f(n)=8(1.5)^{n-1}

    Thus, the function that represents the relationship between n and f(n) is f(n)=8(1.5)^{n-1}

    Therefore, Option D is the correct answer.

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45:7+7-4:2-5:5*4+35:2 =? ( )