Solve the problem.
-After a new product is launched the cumulative sales $S ( t )$ (in $\$ 1000 ) t$ weeks after launch is given by:
$$S ( t ) = \frac { 64 } { 1 + 8 e ^ { - 0.47 t } }$$
What is the limiting value in sales?
A) $\$ 8,000$
B) $\$ 64,000$
C) $\$ 6,000$
D) $\$ 47,000$

Question

Quizplus · Accepted Answer

The limiting value in sales is found by taking the limit of $S(t)$ as $t$ approaches infinity. As $t$ goes to infinity, $e^{-0.47t}$ approaches 0, making the denominator $1 + 8(0) = 1$. Thus, the limiting value is $S(t) = \frac{64}{1} = 64$ in $1000, which is $\$64,000$.

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