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23 October, 20:25

The population of a city is modeled by the equation P (t) = 256,114e0.25t where t is measured in years. If the city continues to grow at this rate, how many years will it take for the population to reach one million?

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  1. 23 October, 23:18
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    Answer: it take 5.448 years for the population to reach one million.

    Step-by-step explanation:

    The population of a city is modeled by the equation

    P (t) = 256,114e0.25t

    where t is measured in years.

    For the population to reach 1000000, it means that

    1000000 = 256114e0.25t

    1000000/256114 = e0.25t

    3.9045 = e0.25t

    Taking ln of both sides of the equation, it becomes

    Ln 3.9045 = Ln e0.25t

    1.362 = 0.25t

    t = 1.362/0.25

    t = 5.448 years
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