Solve the problem.
-After a new product is launched the cumulative sales $S ( t )$ (in $\$ 1000 ) t$ weeks after launch is given by
$$S ( t ) = \frac { 54 } { 1 + 11 e ^ { - 0.32 t } }$$
Determine the amount of time for the cumulative sales to reach $\$ 48,000$. Round to the nearest week.
A) 14 weeks
B) 1 week
C) 27 weeks
D) 54 weeks

Question

Quizplus · Accepted Answer

To find the time $ t $ when sales reach \$48,000, set $ S(t) = 48 $ (since sales are in thousands) and solve for $ t $:  $$ 48 = \frac{54}{1 + 11e^{-0.32t}} $$  Solving this equation gives $ t \approx 14 $ weeks.

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