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math

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the population of a southern city follows the exponential law. If the population doubled in size over an 18 month period and the current population in 10000, what will be the population 2 years from now?

the equation for the exponential equation is: A=ao e ^ -kt

ao is the original amount

a is what the population will be

t is the amount of time

k is the rate of growth

  • math - ,

    I don't see why the exponent is negative since this an exponentional growth, the negative usually indicates decay.

    Anyway...
    I would use A = a (e^kt), where t is months
    using << the population doubled in size over an 18 month period >>
    2 = 1(e^18k)
    ln 2 = 18k
    k = ln 2/18

    so A = 1000 (e^(24*ln2/18))
    = 1000(2.51984)
    = 2520

    another way would be to use

    A = 1000(2)t/k and put in t=24
    A = 1000(2^1.3333333)
    = 2520

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