Solve the problem.
-A publishing company has published a new magazine for young adults. The monthly sales S (in thousands) is given by where t is the number of months since the first issue was published. Find S(3) and S'(3) and
Interpret the results.
A) At three months, the monthly sales are $480,000 and increasing at 64,000 magazines per month.
B) At three months, the monthly sales are $480,000 and decreasing at 64,000 magazines per month.
C) At three months, the monthly sales are $2, 400,000 and increasing at 64,000 magazines per month.
D) At three months, the monthly sales are $2,400,000 and increasing at 800,000 magazines per month.

Question

Solve the problem.
-A publishing company has published a new magazine for young adults. The monthly sales S (in thousands) is given by  where t is the number of months since the first issue was published. Find S(3) and S'(3) and
Interpret the results.
A) At three months, the monthly sales are $480,000 and increasing at 64,000 magazines per month. 
B) At three months, the monthly sales are $480,000 and decreasing at 64,000 magazines per month. 
C) At three months, the monthly sales are $2, 400,000 and increasing at 64,000 magazines per month. 
D) At three months, the monthly sales are $2,400,000 and increasing at 800,000 magazines per month.

Quizplus · Accepted Answer

To find S(3) we substitute t=3 into the given function:
S(3) = 11ebb6d7_48ba_fd34_b437_e9b3f7252859_TB8593_11 = 11 x 3^2 x e^(0.05 x 3) = $480,000.
To find S'(3) we differentiate the given function:
S'(t) = 22t x e^(0.05t) + 11t^2 x 0.05 x e^(0.05t)
S'(3) = 22 x 3 x e^(0.05 x 3) + 11 x 3^2 x 0.05 x e^(0.05 x 3) = 64,128.
Therefore, at three months, the monthly sales are $480,000 and increasing at 64,000 magazines per month.

Solve the Problem. -A Publishing Company Has Published a New Magazine for Young