In an effort to control vegetation overgrowth, 114 rabbits are released in an isolated area free of predators. After 3 years, it is estimate

Question

In an effort to control vegetation overgrowth, 114 rabbits are released in an isolated area free of predators. After 3 years, it is estimated that the rabbit population has increased to 912. Assuming exponential population growth, what will the population be after another 3 months? Round to the nearest rabbit.

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    2021-09-08T23:19:09+00:00

    114 rabbits are released in an isolated area free of predators

    When month =0 , the rabbits = 114

    3 years = 36 months

    When months = 36 , then rabbits = 912

    (0,144) and (36, 912)

    Exponential growth equation is y = ab^x

    Plug in each point and solve for ‘a’  and ‘b’

    114= ab^0  so a= 114

    (36, 912)

    912= 114b^{36}

    Divide both sides by 114 and then take 36th root on both sides

    8 = b^36

    b = 1.05946

    so exponential equation is y= 114(1.05946)^x

    x is the number of months and y is the population

    to find the population be after another 3 months

    Plug in 36+3= 39 for x  and find out y

    y= 114(1.05946)^{39}

    y= 1084.43336

    so , 1084 rabbits after another 3 months

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