A species of animal is discovered on an island. Suppose that the population size P(t) of the species can be modeled by the following functio

Question

A species of animal is discovered on an island. Suppose that the population size P(t) of the species can be modeled by the following function, where time t is measured in years.
P(t) =800/1+ 3e^-0.29t.
Find the initial population size of the species and the population size after 10 years. Round your answers to the nearest whole number as necessary.

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Khang Minh 2 months 2021-08-18T07:08:41+00:00 1 Answers 1 views 0

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    2021-08-18T07:10:01+00:00

    Answer:

    The initial population is 200

    The population after 10 years is 687

    Step-by-step explanation:

    Given

    P(t) =\frac{800}{1+ 3e^{-0.29t.}}

    Solving (a): The initial population

    Here:

    t = 0

    Substitute 0 for t in P(t)

    P(0) =\frac{800}{1+ 3e^{-0.29*0}}

    P(0) =\frac{800}{1+ 3e^{0}}

    P(0) =\frac{800}{1+ 3*1}

    P(0) =\frac{800}{1+ 3}

    P(0) =\frac{800}{4}

    P(0) =200

    The initial population is 200

    Solving (b): Population after 10 years.

    Here

    t = 10

    Substitute 10 for t in P(t)

    P(10) =\frac{800}{1+ 3e^{-0.29*10}}

    P(10) =\frac{800}{1+ 3e^{-2.9}}

    P(10) =\frac{800}{1+ 3*0.055}

    P(10) =\frac{800}{1+ 0.165}

    P(10) =\frac{800}{1.165}

    P(10) =687 — approximated.

    The population after 10 years is 687

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