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Math Help - Doubling time

  1. #1
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    Doubling time

    Mike raises mink, which reproduce exponentially. He currently has 50 mink in his garage, where a month ago he had only 40.
    How long does it take the number of mink to double?

    ok so the rate is  (50-40)/40 = 0.25

     100 = 50e^{0.25T}

     <br />
T=4ln2<br />
<---- is this 4ln2 month or 4ln2 year?
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  2. #2
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    Quote Originally Posted by cammywhite View Post
    Mike raises mink, which reproduce exponentially. He currently has 50 mink in his garage, where a month ago he had only 40.
    How long does it take the number of mink to double?

    ok so the rate is  (50-40)/40 = 0.25

     100 = 50e^{0.25T}

     <br />
T=4ln2<br />
<---- is this 4ln2 month or 4ln2 year?
    How do you figure?

    We are told that they reproduce exponentially so the equation is of the form

    y=Ca^t

    we know that at t=0 y=40

    40=Ca^{0} \iff 40 = C

    y=40a^{t} then in one month t=1 y=50

    50=40a^{1} \iff a=\frac{5}{4}

    So the equation is

    y=40\left( \frac{5}{4}\right)^t

    we want to know when y=80

    80=40\left( \frac{5}{4}\right)^{t}

    Now all we need to do is solve this equation for t.
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