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13 October, 03:48

The population of a small town is currently 6000. This population grows at roughly 1.6% per year. In how many years will the population of the town triple?

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  1. 13 October, 05:16
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    Answer: it will triple in 69.1 years.

    Step-by-step explanation:

    The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

    A = P (1 + r) ^t

    Where

    A represents the population after t years.

    t represents the number of years.

    P represents the initial population.

    r represents rate of growth.

    From the information given,

    P = 6000

    A = 3 * 6000 = 18000

    r = 1.6% = 1.6/100 = 0.016

    Therefore

    18000 = 6000 (1 + 0.016) ^t

    18000/6000 = (1.016) ^t

    3 = (1.016) ^t

    Taking log of both sides to base 10

    Log 3 = log1.016^t = tlog1.016

    0.477 = 0.0069t

    t = 0.477/0.0069

    t = 69.1 years
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