precalculus

A population doubles every 30 years. Assuming exponential growth find the following:

annual growth rate: %
continuous growth rate: %

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  1. 2 = 1(1+i)^20
    take 20th root of both sides
    1.03526 = 1+i
    i = .03526

    the rate is 3.526%

    continuous growth:
    2 = e^(20k)
    ln 2 = 20k(lne)
    k = ln2/20 = .03466 or 3.466%

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