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29 June, 19:06

In 2010 Small Town's population was 1,759 people. If it's declining by 2% each year, what would be the population in 2020? how long till the population is less than 1,000?

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  1. 29 June, 21:43
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    If the population decreases by 2% each year, that can be represented by multiplying the population by 0.98 mathematically. So if it decreases by 2% each year, an equation we can use is:

    P * (0.98) ^t,

    where P is the current population and t is the number of years.

    So in 2020, that would be 10 years from now, so the population would be:

    1759 * (0.98) ^10 = 1437.23

    Or about 1437 people.

    How long till it is less than 1000? We can set up an inequality and solve:

    1759 * (0.98) ^t < 1000

    (0.98) ^t < 1000/1759

    t*ln (0.98) < ln (1000/1759)

    t > ln (1000/1759) / (ln (0.98)) (swap the sign because ln (0.98) is a negative #)

    t > 27.95

    So the population would be below 1000 in about 28 years, or 2038.
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