Revenue Growth The demand for the Cyberpunk II arcade video game is modeled by the logistic curve q ( t ) = 10 , 000 1 + 0.5 e − 0.4 t , where q ( t ) is the total number of units sold t months after its introduction. a. Use technology to estimate q ' ( 4 ) . b. Assume that the manufacturers of Cyberpunk II sell each unit for $ 800 . What is the company’s marginal revenue d R / d q ? c. Use the chain rule to estimate the rate at which revenue is growing 4 months after the introduction of the video game.
Revenue Growth The demand for the Cyberpunk II arcade video game is modeled by the logistic curve q ( t ) = 10 , 000 1 + 0.5 e − 0.4 t , where q ( t ) is the total number of units sold t months after its introduction. a. Use technology to estimate q ' ( 4 ) . b. Assume that the manufacturers of Cyberpunk II sell each unit for $ 800 . What is the company’s marginal revenue d R / d q ? c. Use the chain rule to estimate the rate at which revenue is growing 4 months after the introduction of the video game.
Solution Summary: The author calculates the value of qprime (4) using technology.
The demand for a certain video game is modeled by the logistic curve
q(t) =
10,000
1 + 0.5e−0.3t
,
where q(t) is the total number of units sold t months after its introduction.
(a)
Use technology to estimate q'(4). (Round your answer to the nearest whole number.)
q'(4) = units per month
(b)
Assume that the manufacturers of the video game sell each unit for $700. What is the company's marginal
revenue dR/dq?
dR
dq
= $ per unit
(c)
Use the chain rule to estimate the rate at which revenue is growing 4 months after the introduction of the video game. (Round your answer to the nearest thousand.)
$ per month
A new fertilizer is being tested on a stalk of corn. The height of the corn is increasing in a linear fashion during the test period. The height of the corn t days after the fertilizer is first applied is given by H = 13 + 1.4t centimeters. Explain in practical terms the meaning of the initial value and growth rate.
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