college algebra

Suppose that the Russian population is declining by 0.48% each year, and continues to decline at this rate every year.

a.) what is the overall 'growth' factor (really a decline factor) for 40 years of population decline? As a percentage of the current population, what will the Russian population be 40 years from now?

b.) by what overall percentage will the population decline over the next 40 years?

c.) look again at part b of this question. Suppose that someone makes the argument: "if the Russian population declines by 0.48% each year, then after 210 years there won't be any population left, since (0.48%)(210) is greater than 100%" What is wrong with this argument?

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  1. well, clearly the population, starting from an initial value of P, is

    p(t) = P(0.9952^t)

    after t years. So,
    p(40)/P = 0.9952^40 = 0.8249
    That makes a decrease of 17.51%

    I think you can now refute the argument about zero population.

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