the percent of births to unmarried women during the period f

the percent of births to unmarried women during the period from 1990 through 2002 can be approximate by the polynomial function defined by f(x)=0.010x^3-0.245x^2+2.09x+26.6, where x=0. represents 1990, x=1 represents 1991, x=1 represents 1991, and so on. use this function to approximate the percent (to the nearest tenth) of births to unmarried women in each given year. a) 1990 b) 1995 c) 2002

Solution

The percentage of births to unmarried women during the period from 1990 to 2002 is represented by f(x) = 0.010x³ - 0.245x² + 2.09x + 26.6 , where x=0. represents 1990, x=1 represents 1991, x=1 represents 1991, and so on.

a) The percentage of births to unmarried women in 1990 = 0.010* 0³ - 0.245*0² + 2.09*0 + 26.6 = 26.6 %

b) The percentage of births to unmarried women in 1995 =  0.010* 5³ - 0.245* 5² + 2.09*5 + 26.6 = 0.010*125 - 0.245*25 + 10.45 + 26.60 = 1.25 - 6.125 + 37.05 = 32.175 = 32.18 %

c) The percentage of births to unmarried women in 2002 =  0.010* 12³ - 0.245*12² + 2.09*12 + 26.6 = 0.010*1728 - 0.245*144 + 25.08+26.60 = 17.28 - 35.28 + 51.68 = 33.68 %