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The Demand for the Cyberpunk II Arcade Video Game Is q(t)=13,0001+0.6e0.5tq ( t ) = \frac { 13,000 } { 1 + 0.6 e ^ { - 0.5 t } }

question 45

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The demand for the Cyberpunk II arcade video game is modeled by the logistic curve q(t) =13,0001+0.6e0.5tq ( t ) = \frac { 13,000 } { 1 + 0.6 e ^ { - 0.5 t } }
Where q(t) q ( t ) is the total number of units sold t months after the game's introduction.

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

Assume that the manufacturers of Cyberpunk II sell each unit for $900. What is the company's marginal revenue, dR dq\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.

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