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10 November, 14:37

The population of a country in 2005 was 25 million. In 2010 it was 31 million. estimate the population in 2020. Use the formula P=Ae^kt

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  1. 10 November, 14:46
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    What you must do is evaluate the function for the given conditions and thus be able to find the constants A and k

    25 = Ae ^ k (2005)

    31 = Ae ^ k2010

    We then have two equations with two unknowns.

    Solving.

    25/31 = e ^ k (2005-2010)

    Ln (25/31) = k (2005-2010)

    k = Ln (25/31) / (2005-2010) = 0.043

    Substituting k in any of the equations:

    25 = Ae ^ (0.043 * (2005))

    Clearing A

    A = 25 / (e ^ (0.043 * (2005))) = 9.02E-37

    Then, by 2020

    P = (9.02E-37) e ^ (0.043 * (2020)) = 48 million

    answer

    the population for 2020 will be 48 million
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