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March 26, 2017

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A population grows exponentially. If the population is 0.5sqrt(e) at one year and 0.5e at two years, what is it at 4 years?

  • Math Calculus Help - ,

    we know that

    p = ae^kt

    using the known values,

    √e/2 = ae^k
    e/2 = ae^2k

    divide to get

    (e/2) / (√e/2) = e^k
    √e = e^k
    so, k = 1/2

    now, we see that
    √e/2 = ae^(1/2)
    so a = 1/2

    p(t) = 1/2 e^(t/2)

    p(4) = 1/2 e^2

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