The sales of a new product (in items per month) can be approximated by $S ( x ) = 400 + 300 \log ( 3 t + 1 )$ , where t represents the number of months after the item first becomes available. Find the number of items sold per
Month 33 months after the item first becomes available.
A) 1000 items per month
B) 6400 items per month
C) 120,000 items per month
D) 3400 items per month

Question

Quizplus · Accepted Answer

To find the number of items sold 33 months after the item first becomes available, substitute $t = 33$ into the given formula: $S(33) = 400 + 300 \log(3(33) + 1)$. This simplifies to $S(33) = 400 + 300 \log(100)$, and since $\log(100) = 2$, the equation further simplifies to $S(33) = 400 + 300(2) = 1000$. Therefore, 1000 items are sold per month 33 months after the item first becomes available.

The Sales of a New Product (In Items Per Month) S(x)=400+300log⁡(3t+1)S ( x ) = 400 + 300 \log ( 3 t + 1 )S(x)=400+300log(3t+1)

The Sales of a New Product (In Items Per Month) $S ( x ) = 400 + 300 \log ( 3 t + 1 )$