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9 May, 19:14

The population of Smalltown in the year 1890 was 6,250. Since then, it has increased at a rate of 3.75% each year. • What was the population of Smalltown in the year 1915? • In 1940? • What will the population of Smalltown be in the year 2003? • When will the population reach 1,000,000 (to the nearest year) ?

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  1. 9 May, 19:23
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    year 1915 : 15,689 year 1940 : 39,381

    t = 137.9 years

    Step-by-step explanation:

    Hi, to answer this question we have to apply an exponential growth function:

    A = P (1 + r) t

    Where:

    p = original population

    r = growing rate (decimal form)

    t = years

    A = population after t years

    Replacing with the values given:

    A = 6,250 (1 + 3.75/100) ^t

    A = 6,250 (1 + 0.0375) ^t

    A = 6,250 (1.0375) ^t

    So, by the year 1915:

    1915-1890 = 25 years passed (t)

    A = 6,250 (1.0375) ^25

    A = 15,689

    by the year 1940:

    1940-1890 = 50 years passed (t)

    A = 6,250 (1.0375) ^50

    A = 39,381

    When will the population reach 1,000,000?. We have to subtitute A=1000000 and solve for t.

    1,000,000 = 6,250 (1.0375) ^t

    1,000,000 / 6,250 = (1.0375) ^t

    160 = 1.0375^t

    log 160 = log 1.0375^t

    log 160 = (t) log 1.0375

    log160 / log 1.0375 = t

    t = 137.9 years
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