A study of the annual population of gray squirrels in a Texas state park shows the population, S(t), can be represented by the function S(t)

Question

A study of the annual population of gray squirrels in a Texas state park shows the population, S(t), can be represented by the function S(t) = 273(1.073)t , where the t represents the number of years since the study started. Based on the function, what is the growth rate? A) 1 B) 0.073 C) 1.073 D) 273

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Josephine 2 weeks 2022-01-10T19:32:11+00:00 1 Answer 0 views 0

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    2022-01-10T19:33:28+00:00

    Option B

    Growth rate is 0.073

    Solution:

    Given that,

    A study of the annual population of gray squirrels in a Texas state park shows the population, S(t), can be represented by the function:

    S(t) = 273(1.073)^t

    where the t represents the number of years since the study started

    We have to find the growth rate

    The growth function is given as:

    y = a(1+r)^t

    Where,

    a is the initial value

    r is the growth rate

    t is the number of years

    Therefore, on comparing we get,

    1 + r = 1.073\\\\r = 1.073 - 1\\\\r = 0.073

    Thus the growth rate is 0.073

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