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28 September, 11:25

In a certain area the consumption of electricity has increased at a continuous rate of 8%. If it continued to increase at this rate, find the number of years before three times as much electricity would be needed

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  1. 28 September, 13:05
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    It will take 14.3 years

    Step-by-step explanation:

    Let the consumption of electricity presently be X kw/h

    In the next three years, we would be expecting an increase to 3x kw/h

    Since we do not know the number of years it will take, let us represent this by t years.

    We can represent the consumption in the next three years by the equation;

    x * (1 + 8%) ^t = 3x

    (1+0.08) ^t = 3

    (1.08) ^t = 3

    We can use natural logarithms to get what t is

    take the natural logarithm of both sides

    ln (1.08) ^t = ln3

    tln1.08 = ln3

    t = ln3/ln1.08 = 1.0986/0.077

    t = 14.3 years
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