The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models $N ( t ) = 0.194 t ^ { 3 } - 7.88 t ^ { 2 } + 15.9 t + 372$ and $M ( t ) = 0.034 t ^ { 3 } - 0.21 t ^ { 2 } + 4.7 t + 171$ where $t$ represents the year, with $t = 0$ corresponding to 2000 . Find and interpret $( N + M ) ( t )$.
A) $( N + M ) ( t ) = 0.228 t ^ { 3 } + 8.09 t ^ { 2 } - 20.6 t - 543$, which represents the total number of Navy and Marines personnel combined.
B) $( N + M ) ( t ) = 0.228 t ^ { 3 } + 8.09 t ^ { 2 } + 20.6 t + 543$, which represents the total number of Navy and Marines personnel combined.
C) $( N + M ) ( t ) = 0.228 t ^ { 3 } - 8.09 t ^ { 2 } - 20.6 t - 543$, which represents the total number of Navy and Marines personnel combined.
D) $( N + M ) ( t ) = 0.228 t ^ { 3 } - 8.09 t ^ { 2 } + 20.6 t + 543$, which represents the total number of Navy and Marines personnel combined.
E) $( N + M ) ( t ) = 0.228 t ^ { 2 } - 8.09 t ^ { 3 } - 20.6 t + 543$, which represents the total number of Navy and Marines personnel combined.

Question

Quizplus · Accepted Answer

We have:

$$(N+M)(t) = N(t) + M(t) = (0.194t^3 - 7.88t^2 + 15.9t + 372) + (0.034t^3 - 0.21t^2 + 4.7t + 171)$$

$$= 0.228t^3 - 8.09t^2 + 20.6t + 543$$

Therefore, the best choice is D. This represents the total number of Navy and Marines personnel combined.

The Total Numbers of Navy Personnel N (In Thousands) and Marines