A publishing company has published a new magazine for young adults. The monthly

Question

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

Explanation / Answer

From the question,

S(t)= 800t/(t+2)

where S= Monthly sales

t= number of months since the first issue was published.

S(3)= 800 * 3 / ( 3+2)= 480

If y= u/v then, dy/dx= (v du/dx - u dv/dx)/v2

S(t)= 800t/(t+2)

S' (t)= [( t+2) 800 - ( 800t) (1)]/(t+2)2= ( 800t + 1600 - 800t)/(t+2)2= 1600/(t+2)2

S'(3) = 1600/(3+2)2 =64

As S'(3) is positive, the sales are increasing.

Since the sales is in thousands,

(B) At three months , the monthly sales are $480,000 and increasing at $64000 magzines per month.

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