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    Help with calculus problem

    In a certain culture of bacteria, the number of bacteria increased sixfold in 10h. Assuming natural growth, how long did it take for their number to double?
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    Quote Originally Posted by Abalo View Post
    In a certain culture of bacteria, the number of bacteria increased sixfold in 10h. Assuming natural growth, how long did it take for their number to double?
    This is classic exponential growth so use the equation A(t) = A_0e^{kt}

    where:

    • A(t) = Amount at time t
    • A_0 = Amount at time 0/initial amount
    • k = growth constant
    • t = time


    By definition the amount at time 0 is equal to A_0

    If the increase is sixfold after ten hours we get the following:

    6A_0 = A_0e^{10k} which is equal to 6 = e^{10k}

    From there you can find k

    Once you know your value of k find t using the rearranged equation below and that A_2 =2A_0= A_0e^{kt}

    t = \frac{1}{k} \left[ \ln (A_t) - \ln (A_0)\right]
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