A population of coyotes in a country is represented by the equation w(t)=80(0.98)^t, where t is the number of years since 1998. In what year

Question

A population of coyotes in a country is represented by the equation w(t)=80(0.98)^t, where t is the number of years since 1998. In what year will the population be 50 wolves?

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Luna 3 weeks 2021-11-10T05:59:15+00:00 1 Answer 0 views 0

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    2021-11-10T06:01:06+00:00

    Answer:

    2021

    Step-by-step explanation:

    w(t) = 80(0.98)^t

    w(t) = 50

    50/80 = (0.98)^t

    5/8 = (0.98)^t

    log(5/8) = log((0.98)^t)

    Property of logs allows the exponent to be move to the front so,

    log(5/8) = t*log(0.98)

    solve for t

    t = (log(5/8))/(log(0.98))

    so t = 23.264

    1998 + t = 2021.264

    Round to 2021 because that’s they year it is present in.

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