Question

From 2000 to 2003, the amount of sales (in billions of dollars) of video games G and toys T in the United States can be modeled by the following equations, where n is the number of years since 2000: G = - 0.08n3 + 0.04n2 + 1.2n + 3.5 and T = 0.4n3 - 1.7n2 + 4n + 16. Find the expression S for the total sales.0.32n3 - 1.74n2 + 5.2n + 19.50.32n3 - 1.66n2 + 5.2n + 19.50.32n3 - 1.66n2 + 5.2n + 310.48n3 - 1.66n2 + 5.2n + 19.5

Answer 1

Given the functions:

`\begin{gathered} G(n)=-0.08n^3+0.04n^2+1.2n+3.5 \\ T(n)=0.4n^3-1.7n^2+4n+16 \\ \end{gathered}`

The total sales (S) will be the sum of G and T

`S(n)=(G+T)(n)`

Therefore,

`S(n)=(-0.08n^3+0.04n^2+1.2n+3.5)+(0.4n^3-1.7n^2+4n+16)`

adding component to component, i.e. x^3 with x^3, x^2 with x^2 , x with x and number with number.

`\begin{gathered} S(n)=(-0.08+0.4)n^3+(0.04-1.7)n^2+(1.2+4)n+(3.5+16) \\ S(n)=0.32n^3-1.66n^2+5.2n+19.5 \end{gathered}`

The answer is: B.