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The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke^0.12t where k is a constant and t is the time in years. If the current population is 15,000, in how many years is the population expected to be 37,500? (Round to the nearest year.)

  • Algebra - ,

    37500 = 1 + 15000(e)^.12t

    (the 1 is rather ineffectual in this equation. Are you sure you typed it right way? )

    Anyway, assuming it is correct

    = 36499 = 15000(e)^.12t
    2.4332667 = e^.12t
    .12t = ln 2.4332667
    .12t = .889235
    t = 7.41 yrs or
    in appr 7 years

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