Math

Bacteria experiences exponential growth, increasing 17% every hour. If there are 800 bacteria now, in how many hours will there be 2000? How would I go about this problem?

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  1. dx/dt = .17x
    dx/x = .17 dt
    ln x = .17t + C
    x = e^(.17t+C) = e^C e^.17t
    when t = 0
    800 = e^C e^0 = e^C
    so
    x = 800 e^.17t
    2000 = 800 e^.17t
    2.5 = e^.17 t
    ln 2.5 = .17 t
    t = .916/.17 = 5.39 hr

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