A publishing company has published a new magazine for young adults. The monthly sales S (in thousands) is given by $S ( t ) = \frac { 800 t } { t + 2 }$ 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 $2, 400,000 and increasing at 64,000 magazines per month.
C) At three months, the monthly sales are $2,400,000 and increasing at 800,000 magazines per month.
D) At three months, the monthly sales are $480,000 and decreasing at 64,000 magazines per month.

Question

Quizplus · Accepted Answer

To find $S(3)$, substitute $t = 3$ into the given function: $S(3) = \frac{800 \times 3}{3 + 2} = \frac{2400}{5} = 480$ (in thousands), so the sales are $480,000. To find $S'(t)$, differentiate $S(t)$ with respect to $t$: $S'(t) = \frac{800(t + 2) - 800t}{(t + 2)^2} = \frac{1600}{(t + 2)^2}$. Then, $S'(3) = \frac{1600}{(3 + 2)^2} = \frac{1600}{25} = 64$ (in thousands), indicating the sales are increasing at a rate of 64,000 magazines per month.

A Publishing Company Has Published a New Magazine for Young S(t)=800tt+2S ( t ) = \frac { 800 t } { t + 2 }S(t)=t+2800t​

A Publishing Company Has Published a New Magazine for Young $S ( t ) = \frac { 800 t } { t + 2 }$