Calculus

An investment grows ar a rate of 2.5% each year compounded continuously. Approximately how long will it take the investment to double?

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  1. dx/dt = .025 x
    dx/x = .025 dt

    ln x = .025 t + c

    x = e^(.025 t+c) = e^c e^.025 t

    so x = C e^.025 t
    at t= 0, x = C e^0 = C
    when is x = 2C ???
    2C = C e^.025 x
    e^.025 x = 2
    .025 x = ln 2 = .6931
    x = 27.7 years

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