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31 January, 01:50

The population of a town is 13,000. It decreases at a rate of 5% per year. In about how many years will the population be less than 12,000?

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  1. 31 January, 02:08
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    This is an exponential decay problem.

    Using the equation Y = a * (1-rate) ^time

    where Y is the future value given as 12,000 and a is the starting value given as 13,000.

    The rate is also given as 5%.

    The equation becomes:

    12,000 = 13,000 (1-0.05) ^x

    12,000 = 13,000 (0.95) ^x

    Divide each side by 13000:

    12000/13000 = 0.95^x/13000

    12/13 = 0.95^x

    Use the natural log function:

    x = ln (12/13) / ln (0.95)

    x = 1.56 years. (this will equal 12,000

    Round to 2 years it will be less than 12000.
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