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27 June, 16:39

A country's population in 1990 was 59 million. In 2002 it was 63 million. Estimate the population in 2018 using exponential growth formula. Round your answer to the nearest million

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  1. 27 June, 16:47
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    The formula for exponential growth is P = Ae^kt

    P = new population

    A = starting population

    k is a constant

    and t is number of years.

    e is a logarithm function

    using the 2 known years

    we know 2002-1990 = 12 years

    the population in 2002 was 63 million, population in 1990 was 59 million

    so using the above equation we can solve for k:

    63 = 59e^k12

    divide both sides by 59:

    63/59 = e^k12

    1.06779 = e^k12

    find logorithm of left side to get rid of the e on the right side:

    ln 1.06779 = k12

    0.06559 = k12

    divide both sides by 12 for k:

    k = 0.06559 / 12 = 0.00546644

    now we want to find population in 2018

    2018 - 1990 = 28 years

    so now t = 28 using the same formula we have:

    P = 59e^ (0.00546644*28)

    P = 68.758 million

    rounded to nearest million = 69 million people
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