The sales of a mature product (one which has passed its peak) will decline according to the function $\mathrm { S } ( \mathrm { t } ) = \mathrm { S } _ { 0 } \mathrm { e } ^ { - \mathrm { at } }$, where $\mathrm { t }$ is time in years since the peak sales. Find the sales of a product 17 years after its peak sales if $\mathrm { a } = 0.24$ and $\mathrm { S } _ { 0 } = 50,900$.
A) 3,827,101 units
B) 431 units
C) 64,707 units
D) 861 units

Question

Quizplus · Accepted Answer

To find the sales 17 years after its peak, substitute $t = 17$, $a = 0.24$, and $\mathrm { S } _ { 0 } = 50,900$ into the given formula: $\mathrm { S } ( 17 ) = 50,900 \cdot \mathrm { e } ^ { - 0.24 \cdot 17 }$. Calculating this gives a result close to 861 units.

The Sales of a Mature Product (One Which Has Passed S(t)=S0e−at\mathrm { S } ( \mathrm { t } ) = \mathrm { S } _ { 0 } \mathrm { e } ^ { - \mathrm { at } }S(t)=S0​e−at

The Sales of a Mature Product (One Which Has Passed $\mathrm { S } ( \mathrm { t } ) = \mathrm { S } _ { 0 } \mathrm { e } ^ { - \mathrm { at } }$