aIn 2010 the population of a country was 98 98 million and g

a)In 2010, the population of a country was 98 98 million and growing at a rate of 1.8 % 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 )

b)Polluted water is passed through a series of filters. Each filter removes 76% of the remaining impurities. Initially the water contains impurities at a level of 400 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)

Solution

a)In 2010, t=0

In 2010, the population of a country was 98 million

growing at a rate of 1.8 % => r =0.018

population P , in millions, as a function of t , P(t)=98(1+r)^t

P(t)=98(1+0.018)^t

P(t)=98(1.018)^t

b). Each filter removes 76%=>r =0.76

Initially the water contains impurities at a level of 400ppm

remaining level of impurities, L , after the water has passed through a series of n filters=g(n)=400(1-r)ⁿ

g(n)=400(1-0.76)ⁿ

g(n)=400(0.24)ⁿ