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Math Help - Did I do this bacteria growth problem correctly?

  1. #1
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    Did I do this bacteria growth problem correctly?

    A certain type of bacteria increases continuously at a rate proportional to the number present. if there are 500 bacteria at a given time and 1000 present 2 hours later, how many will there be 5 hours from the initial time given?

    dP/dt = kP
    dP=kPdt
    ∫dP/P = k ∫dt
    ln|P| = kt + C
    P = Ce^kt
    P= P0e^kt
    1000 = 500e^2k
    2 = e^2k
    ln2= 2k
    k=ln(2) /2
    P = 500e^5(ln2/2)
    P=2828.4
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  2. #2
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    Quote Originally Posted by wmw88 View Post
    A certain type of bacteria increases continuously at a rate proportional to the number present. if there are 500 bacteria at a given time and 1000 present 2 hours later, how many will there be 5 hours from the initial time given?

    dP/dt = kP
    dP=kPdt
    ∫dP/P = k ∫dt
    ln|P| = kt + C
    P = Ce^kt
    P= P0e^kt
    1000 = 500e^2k
    2 = e^2k
    ln2= 2k
    k=ln(2) /2
    P = 500e^5(ln2/2)
    P=2828.4
    looks fine.
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