The demand function for a limited edition comic book is given by $p = 3000 \left( 1 - \frac { 5 } { 5 + e ^ { - 0.015 x } } \right)$ Find the price $p$ for a demand of $x = 45$ units.
A)$5722.74
B)$277.26
C)$369.89
D)$340.13
E)$6369.89

Question

Quizplus · Accepted Answer

To find the price $p$ for a demand of $x = 45$ units, substitute $x = 45$ into the demand function:$$p = 3000 \left( 1 - \frac { 5 } { 5 + e ^ { - 0.015 \times 45 } } \right)$$$$p = 3000 \left( 1 - \frac { 5 } { 5 + e ^ { - 0.675 } } \right)$$$$p = 3000 \left( 1 - \frac { 5 } { 5 + 0.509 } \right)$$$$p = 3000 \left( 1 - \frac { 5 } { 5.509 } \right)$$$$p = 3000 \left( 1 - 0.9074 \right)$$$$p = 3000 \times 0.0926$$$$p \approx 277.26$$Therefore, the price $p$ for a demand of $x = 45$ units is approximately $277.26.

The Demand Function for a Limited Edition Comic Book Is p=3000(1−55+e−0.015x)p = 3000 \left( 1 - \frac { 5 } { 5 + e ^ { - 0.015 x } } \right)p=3000(1−5+e−0.015x5​)

The Demand Function for a Limited Edition Comic Book Is $p = 3000 \left( 1 - \frac { 5 } { 5 + e ^ { - 0.015 x } } \right)$