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
$N ( t ) = 0.193 t ^ { 3 } - 3.88 t ^ { 2 } + 15.9 t + 370$ and $M ( t ) = 0.033 t ^ { 3 } - 0.21 t ^ { 2 } + 1.7 t + 171$
Where t represents the year, with t = 0 corresponding to 2000.

Find and interpret $( N + M ) ( t )$ .

A) $( N + M ) ( t ) = 0.226 t ^ { 3 } + 4.09 t ^ { 2 } - 17.6 t - 541$ , which represents the total number of Navy and Marines personnel combined.
B) $( N + M ) ( t ) = 0.226 t ^ { 3 } + 4.09 t ^ { 2 } + 17.6 t + 541$ , which represents the total number of Navy and Marines personnel combined.
C) $( N + M ) ( t ) = 0.226 t ^ { 3 } - 4.09 t ^ { 2 } - 17.6 t - 541$ , which represents the total number of Navy and Marines personnel combined.
D) $( N + M ) ( t ) = 0.226 t ^ { 3 } - 4.09 t ^ { 2 } + 17.6 t + 541$ , which represents the total number of Navy and Marines personnel combined.
E) $( N + M ) ( t ) = 0.226 t ^ { 2 } - 4.09 t ^ { 3 } - 17.6 t + 541$ , which represents the total number of Navy and Marines personnel combined.

Question

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 
 $N ( t ) = 0.193 t ^ { 3 } - 3.88 t ^ { 2 } + 15.9 t + 370$ and $M ( t ) = 0.033 t ^ { 3 } - 0.21 t ^ { 2 } + 1.7 t + 171$  
Where t represents the year, with t = 0 corresponding to 2000.
 
Find and interpret $( N + M ) ( t )$ .
 
A) $( N + M ) ( t ) = 0.226 t ^ { 3 } + 4.09 t ^ { 2 } - 17.6 t - 541$ , which represents the total number of Navy and Marines personnel combined.
B) $( N + M ) ( t ) = 0.226 t ^ { 3 } + 4.09 t ^ { 2 } + 17.6 t + 541$ , which represents the total number of Navy and Marines personnel combined.
C) $( N + M ) ( t ) = 0.226 t ^ { 3 } - 4.09 t ^ { 2 } - 17.6 t - 541$ , which represents the total number of Navy and Marines personnel combined.
D) $( N + M ) ( t ) = 0.226 t ^ { 3 } - 4.09 t ^ { 2 } + 17.6 t + 541$ , which represents the total number of Navy and Marines personnel combined.
E) $( N + M ) ( t ) = 0.226 t ^ { 2 } - 4.09 t ^ { 3 } - 17.6 t + 541$ , which represents the total number of Navy and Marines personnel combined.

Quizplus · Accepted Answer

To find $(N + M)(t)$, add the corresponding coefficients of $N(t)$ and $M(t)$. This results in $0.226t^3 - 4.09t^2 + 17.6t + 541$, representing the combined total of Navy and Marines personnel in thousands.

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