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13 April, 03:16

A country's population in 1993 was 127 million. In 2000 it was 132 million. Estimate the population in 2008 using the exponential growth formula. Round your answer to the nearest million.

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  1. 13 April, 04:31
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    To solve the exponential growth application question we proceed as follows;

    suppose the time, t between 1993 to 2000 is such that in 1993, t=0 and in 2000, t=7.

    Note theta the population is in millions;

    The exponential formula is given by:

    f (t) = ae^ (kt)

    where;

    f (t) = current value

    a=initial value

    k=constant of proportionality

    t=time

    substituting the values we have in our formula we get:

    132=127e^ (7k)

    132/127=e^ (7k)

    introducing the natural logs we get:

    ln (132/127) = 7k

    k=[ln (132/127) ]/7

    k=0.0055

    Thus our formula will be:

    f (t) = 127e^ (0.0055t)

    The population in 2008 will be:

    f (t) = 127e^ (15*0.0055) = 127e^ (0.0825) = 137.922

    Thus the population in 2008 is appropriately 138 million.
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