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10 January, 12:15

Suppose the population of a town is 567 in 2001. The population decreases at a rate of 1.5% every year. What will be the population of the town in 2010?

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  1. 10 January, 14:07
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    Exponential decay can be expressed as:

    f=ir^t, f=final value, i=initial value, r=common ratio (or rate) and t=times rate is applied (or time).

    In this case i=567 and r = (100-1.5) / 100=0.985, so the equation is:

    p (t) = 567 (0.985^t), in this case t=year-2001=y-2001 so we can say:

    p (y) = 567 (0.985) ^ (y-2001) so in the year 2010

    p (2010) = 567 (0.985) ^ (2010-2001)

    p (2010) = 567 (0.985^9)

    p (2010) ≈494.89 (to nearest hundredth)

    Since we are dealing with people, population needs to be an integer amount

    p (2010) ≈495 (to nearest whole person : P)
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