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March 27, 2017

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How long will it take for the population of a certain country to double if its annual growth rate is 1.5%? Round to the nearest year. Use the exponential growth model P(t) = P0e^kt

  • Algebra - ,

    Two ways to do it:
    each year multiply by 1.015 (like compound interest)
    1.015^n = 2
    n log 1.015 = log 2
    n = log 2 / log1.015 = 46.55 years

    or do it the way they said to do it with continuous growth
    dy/dt = .015y
    y = yi e^.015 t
    y/yi = 2 = e^.015 t
    ln 2 = .015 t
    t = 46.2

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