In 2010, the population of a country was 92 million and growing at a rate of 1.8

Question

In 2010, the population of a country was 92 million and growing at a rate of 1.8% per year. Assuming the percentage growth rate remains constant, express the population P, in millions, as a function of t, the number of years after 2010. Let P = f(t). f(t) = b. Polluted water is passed through a series of filters. Each filter removes 80% of the remaining impurities. Initially the water contains impurities at a level of 440 parts per million (ppm). Determine a rule for the function g, that gives the remaining level of impurities, L, after the water has passed through a series of n filters. g(n) =

Explanation / Answer

(a)Given, P0=92 million

rate=r=1.8%=0.018, time = t year

so, P=f(t)=P0(e)^(rt)=92*e^(0.018t)

(b)each filter removes 80% of the remaining impurities.

remaining level of impurity equals 20% of the original impurity

Given initial impurity=440 PPM,   n= no of filter

therfore remaining impurity after n filter

L==g(n)=440*(0.20)^n

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