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
$N ( t ) = 0.194 t ^ { 3 } - 1.88 t ^ { 2 } + 15.9 t + 373 \text { and } M ( t ) = 0.032 t ^ { 3 } - 0.26 t ^ { 2 } + 5.7 t + 172$ where t represents the year, with $t = 0$ corresponding to 2000.
Find and interpret $( N + M ) ( t )$
A) $( N + M ) ( t ) = 0.226 t ^ { 2 } - 2.14 t ^ { 3 } - 21.6 t + 545$, which represents the total number of Navy and Marines personnel combined.
B) $( N + M ) ( t ) = 0.226 t ^ { 3 } + 2.14 t ^ { 2 } + 21.6 t + 545$, which represents the total number of Navy and Marines personnel combined.
C) $( N + M ) ( t ) = 0.226 t ^ { 3 } + 2.14 t ^ { 2 } - 21.6 t - 545$, which represents the total number of Navy and Marines personnel combined.
D) $( N + M ) ( t ) = 0.226 t ^ { 3 } - 2.14 t ^ { 2 } - 21.6 t - 545$, which represents the total number of Navy and Marines personnel combined.
E) $( N + M ) ( t ) = 0.226 t ^ { 3 } - 2.14 t ^ { 2 } + 21.6 t + 545$, which represents the total number of Navy and Marines personnel combined. $( f - g ) ( t + 1 )$

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 
$N ( t ) = 0.194 t ^ { 3 } - 1.88 t ^ { 2 } + 15.9 t + 373 \text { and } M ( t ) = 0.032 t ^ { 3 } - 0.26 t ^ { 2 } + 5.7 t + 172$ where t represents the year, with $t = 0$ corresponding to 2000.
Find and interpret $( N + M ) ( t )$ 
A) $( N + M ) ( t ) = 0.226 t ^ { 2 } - 2.14 t ^ { 3 } - 21.6 t + 545$, which represents the total number of Navy and Marines personnel combined.
B) $( N + M ) ( t ) = 0.226 t ^ { 3 } + 2.14 t ^ { 2 } + 21.6 t + 545$, which represents the total number of Navy and Marines personnel combined.
C) $( N + M ) ( t ) = 0.226 t ^ { 3 } + 2.14 t ^ { 2 } - 21.6 t - 545$, which represents the total number of Navy and Marines personnel combined.
D) $( N + M ) ( t ) = 0.226 t ^ { 3 } - 2.14 t ^ { 2 } - 21.6 t - 545$, which represents the total number of Navy and Marines personnel combined.
E) $( N + M ) ( t ) = 0.226 t ^ { 3 } - 2.14 t ^ { 2 } + 21.6 t + 545$, which represents the total number of Navy and Marines personnel combined. $( f - g ) ( t + 1 )$

Quizplus · Accepted Answer

To find $(N+M)(t)$, we simply add the two functions together:

$$(N+M)(t)=N(t)+M(t)=0.194t^3-1.88t^2+15.9t+373 + 0.032t^3-0.26t^2+5.7t+172$$

Combining like terms, we get:

$$(N+M)(t)=0.226t^3-2.14t^2+21.6t+545$$

Therefore, the best choice is E.

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