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Thread: 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 $\displaystyle (50-40)/40 = 0.25$

    $\displaystyle 100 = 50e^{0.25T}$

    $\displaystyle
    T=4ln2
    $ <---- is this 4ln2 month or 4ln2 year?
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  2. #2
    Behold, the power of SARDINES!
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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 $\displaystyle (50-40)/40 = 0.25$

    $\displaystyle 100 = 50e^{0.25T}$

    $\displaystyle
    T=4ln2
    $ <---- 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

    $\displaystyle y=Ca^t$

    we know that at t=0 y=40

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

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

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

    So the equation is

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

    we want to know when y=80

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

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