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24 January, 04:07

The rate of change of the population of a city is proportional to the population P at any time t (in years). In 2000, the population was 200,000, and the constant of proportionality was 0.013. Estimate the population of the city in the year 2025.

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  1. 24 January, 05:41
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    276,806

    Step-by-step explanation:

    In this context "rate of change of the population ... is proportional to the population" means it can be modeled by ...

    P (t) = P0·e^ (kt)

    where "k" is the "constant of proportionality, and P0 is the population corresponding to t=0.

    Filling in the given numbers, we have ...

    P (25) = 200,000·e^ (0.013·25) ≈ 276,806

    The population is estimated to be 276,806 in the year 2025.
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