The Demand for the Cyberpunk II Arcade Video Game Is $q ( t ) = \frac { 13,000 } { 1 + 0.6 e ^ { - 0.5 t } }$

Multiple Choice

The demand for the Cyberpunk II arcade video game is modeled by the logistic curve $q ( t ) = \frac { 13,000 } { 1 + 0.6 e ^ { - 0.5 t } }$
Where $q ( t )$ is the total number of units sold t months after the game's introduction.

Use technology to estimate $q ^ { \prime } ( 9 )$ .

Assume that the manufacturers of Cyberpunk II sell each unit for $900. What is the company's marginal revenue, $\frac { \mathrm { d } R } { \mathrm {~d} q }$

Use the chain rule to estimate the rate at which revenue is growing 9 months after the introduction of the video game.

Please round each answer to the nearest whole number.

A) $\frac { \mathrm { d } q } { \mathrm {~d} t } = 43 , \frac { \mathrm { d } R } { \mathrm {~d} q } = 900 , \frac { \mathrm { d } R } { \mathrm {~d} t } = 38,734$
B) $\frac { \mathrm { d } q } { \mathrm {~d} t } = 43 , \frac { \mathrm { d } R } { \mathrm {~d} q } = 900 , \frac { \mathrm { d } R } { \mathrm {~d} t } = 38,478$
C) $\frac { \mathrm { d } q } { \mathrm {~d} t } = 71 , \frac { \mathrm { d } R } { \mathrm {~d} q } = 700 , \frac { \mathrm { d } R } { \mathrm {~d} t } = 64,130$
D) $\frac { \mathrm { d } q } { \mathrm {~d} t } = 86 , \frac { \mathrm { d } R } { \mathrm {~d} q } = 800 , \frac { \mathrm { d } R } { \mathrm {~d} t } = 76,956$
E) $\frac { \mathrm { d } q } { \mathrm {~d} t } = 143 , \frac { \mathrm { d } R } { \mathrm {~d} q } = 900 , \frac { \mathrm { d } R } { \mathrm {~d} t } = 128,260$