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Math Help - Help on Problem! Algebra 2

  1. #1
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    Help on Problem! Algebra 2

    in 1859, 24 wild rabbits were brought to Australia and released. This original population of 24 rabbits grew to an estimated 600,000,000 by 1950.

    a) Assuming that the growth in the rabbit population is exponential over these years, find a model to describe the number of rabbits in Australia during this time period.

    b) Did the Population of rabbits in Australia continue to grow at such a fast pace after 1950?

    Thanks
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ep78 View Post
    in 1859, 24 wild rabbits were brought to Australia and released. This original population of 24 rabbits grew to an estimated 600,000,000 by 1950.

    a) Assuming that the growth in the rabbit population is exponential over these years, find a model to describe the number of rabbits in Australia during this time period.

    b) Did the Population of rabbits in Australia continue to grow at such a fast pace after 1950?

    Thanks
    Well assuming an exponential model
    A(t) = A_0 * exp{bt}

    At t = 0 we have
    A(0) = 24 * exp(b * 0} = 24

    So
    A(t) = 24 * exp{bt}

    In 1950 we have t = 1950 - 1859 = 91

    So
    600 000 000 = 24 * exp{91t}

    Divide both sides by 24 and take the natural log of both sides:
    91t = ln(25 000 000)

    Now solve for t.

    As for can the rate keep up, what is A(92)? A(93)? Do these numbers make sense?

    -Dan
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  3. #3
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    Quote Originally Posted by topsquark View Post
    Well assuming an exponential model
    A(t) = A_0 * exp{bt}

    At t = 0 we have
    A(0) = 24 * exp(b * 0} = 24

    So
    A(t) = 24 * exp{bt}

    In 1950 we have t = 1950 - 1859 = 91

    So
    600 000 000 = 24 * exp{91t}

    Divide both sides by 24 and take the natural log of both sides:
    91t = ln(25 000 000)

    Now solve for t.

    As for can the rate keep up, what is A(92)? A(93)? Do these numbers make sense?

    -Dan
    So, the model would be the answer of this....[91t=ln(25,000)] after you solve for t? or would that be the answer for "c"?

    Thanks Again
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