Some companies spend billions of dollars each year lobbying Congress to secure some desired action. For the years 1998-2012, the number of unique, registered lobbyists who have actively lobbied Congress can be approximated with the 4th -degree polynomial model N (t) = − 0.35 t^4 + 6.1t^3 − 33 t^2 + 460t + 12278 0 ≤ t ≤ 15

where t represents the number of years since the beginning of the year 1998. Round your answers to the nearest lobbyist.

Required:
a. How many lobbyists were there during the 15-year deal?
b. If this trend continues, how many lobbyists can be expected from 2013 to 2016?

Step-by-step explanation:

Given the number of unique, registered lobbyists who have actively lobbied Congress can be approximated with the 4th -degree polynomial model

N(t) = − 0.35 t⁴ + 6.1t³ − 33 t² + 460t + 12278 0 ≤ t ≤ 15  where;

t = number of years since the beginning of the year 1998

a) To determine the number of lobbyists were there during the 15-year deal, we will have to substitute t = 15 into the modeled equation as shown;

N(15) = − 0.35 (15)⁴ + 6.1(15)³ − 33(15)² + 460(15) + 12278

N(15) = -17,718.75+20,587.5-7,425+6,900+12278

N(15) = 14,621.75

This shows that there are about 14,622 lobbyists during the 15-year deal

b) To determine the number of lobbyists that can be expected from 2013 to 2016 if the trend continue, we will substitute t =3 into the modeled equation since there are 3 years between 2012 and 2016.

N(3) = − 0.35 (3)⁴ + 6.1(3)³ − 33(3)² + 460(3) + 12278

N(3) = -28.35+164.7-297+1380+12279

N(3) = 13498.35

This means that if the trend continues, about 13,498 lobbyists will be expected from 2013 to 2016.