The population of a country was 96 million and growing at a

The population of a country was 96 million and growing at a rate of 2% 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). Polluted water is passed through a series of filters. Each filter removes 67% of the remaining impurities. Initially the water contains impurities at a level of 460 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.

Solution

(1) Given Po=96, r=2%=0.02 inreasing =0.02 time is t

Therefore P=f(t)= Po(1+r)^t=96(1+0.02)^t=96*1.02^t

(2)Given g(o)=460, r=67%=0.67 dereasing =-0.67 time is t and

Therefore P=f(t)= Po(1+r)^t=460(1-0.67)^t=460* 0.33^t