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22 September, 15:01

A town has a population of 20000 and grows at 4.5% every year. To the nearest tenth of a year, how long will it be until the population will reach 42800?

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  1. 22 September, 15:25
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    Answer:17.3 years

    Step-by-step explanation:

    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,

    A = 42800

    P = 20000

    r = 4.5% = 4.5/100 = 0.045

    Therefore

    42800 = 20000 (1 + 0.045) ^t

    42800/20000 = (1.045) ^t

    2.14 = (1.045) ^t

    Taking log of both sides to base 10

    Log 2.14 = log1.045^t = tlog1.045

    0.3304 = t * 0.0191

    0.3304 = 0.0191t

    t = 0.3304/0.0191

    t = 17.3 years
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