math

The population of Knoxville is 500,000 and is increasing at the rate of 3.75% each year. Approximately when will the population reach 1 million? Use an exponential model to solve the problem.

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  1. dp/dt = .0375 people/year

    ln p = .0375 t + c

    p = c e^(.0375 t)
    when t = 0, p = 500,000
    so
    p = 500,000 e^(.0375 t)

    so
    2 = 1,000,000/500,000 = e^(.0375 t)
    ln 2 = .0375 t

    t = 18.5 years

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