The number of embroideries that a girl can make per year since 1996 can be modeled by the function N(t) =3t+20 and the price per embroidery can be modeled by P(t)=3t(2)-8t+55 model what's a girl's total amount of income generated by making embroideries in 1999? Round your answer to the nearest cent

Given number of embroideries N(t) = 3t+20, where t is the number of years since 1996.

So in 1999, number of embroideries , N(3)= 3*3+20

                                                             = 29

Given price per embroidery [tex]P(t) = 3t^{2} -8t+55[/tex]

So in 1999, price per embroidery is [tex]P(3)= 3*3^{2} -8*3+55 = 82-24 = 58[/tex]

Hence income = P(3)*N(3) = 58*29 = 1682