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.
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Find and interpret $( N + M ) ( t )$ .
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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 $(N + M)(t)$, you add the corresponding coefficients of the $N(t)$ and $M(t)$ polynomials. This results in $0.226t^3 - 4.09t^2 + 17.6t + 541$, which represents the total number of Navy and Marines personnel combined in thousands.

The Total Numbers of Navy Personnel N (In Thousands)and Marines N(t)=0.193t3−3.88t2+15.9t+370N ( t ) = 0.193 t ^ { 3 } - 3.88 t ^ { 2 } + 15.9 t + 370N(t)=0.193t3−3.88t2+15.9t+370

The Total Numbers of Navy Personnel N (In Thousands)and Marines $N ( t ) = 0.193 t ^ { 3 } - 3.88 t ^ { 2 } + 15.9 t + 370$