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23 May, 21:30

The exponential model A=429e 0.024t describes the population, A, of a country in millions, t years after 2003. Use the model to determine when the population of the country will be 559 million.

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  1. 23 May, 21:49
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    Year 2,590

    Step-by-step explanation:

    In this question, we are asked to calculate the year at which the population of a country will be a certain amount given the exponential equation through which the equation proceeds.

    Let's rewrite the exponential function;

    A = 429e^0.024t

    Now here, our A is 559,000,000

    t is unknown

    Let's substitute this value of A in the exponential equation;

    559,000,000 = 429 * e^0.024t

    559,000,000/429 = e^0.024t

    1,303,030.303030303 = e^0.024t

    Let's take the logarithm of both sides to base e, we have;

    ln (1,303,030.303030303) = ln (e^0.024t)

    14.08 = 0.024t

    t = 14.08/0.024

    t = 587 years

    Now, we add this to year 2003 and this gives year 2590
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