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A company's revenue from selling x units of a new software game is R(x)=1000x-20x^2 dollars. if sales are increasing at a rate of 50 units per day, find how fast the revenue is growing at a time when 20 units have been sold.

 Jul 19, 2019
 #1
avatar+18754 
+2

Do you know calculus?

You need the RATE of revenue growth.....this is the SLOPE of the revenue function at x = 20

The DERIVATIVE of the revenue funtion will give you the slope

the derivative is  R'(x) = 1000 - 40x       at x = 20     this equals 200 dollars/unit   (edited.....had wrong units )

    200 dollars/unit x 50 units/day = 10000/day     thank you

 Jul 19, 2019
edited by Guest  Jul 19, 2019
edited by Guest  Jul 19, 2019
 #4
avatar+102774 
0

Guest do not change your answer without stating what you have changed.

It is confusing.

Melody  Jul 19, 2019
edited by Melody  Jul 19, 2019
 #7
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Sorry...fixed it....was fixing it before anyone had yet posted, so I didn't bother.   ~EP

Guest Jul 19, 2019
 #2
avatar+19 
0

I have been studying Calculus for 13 YEARS! this is a question that is far beyond my years of experience. Do i know calculus?? YES i have 4 masters of Calculus, the answer is 10k per day by the way, thankyou very much.

 Jul 19, 2019
 #3
avatar+102774 
+2

Guest was just trying to be helpful. No need to be snarly about it.

I had the same thoughts as them to start with.

 

\(R=1000x-20x^2\\ \frac{dx}{dt}=50\\ Find \;\;\frac{dR}{dt}\;\;when\;\;x=20\\~\\ \frac{dR}{dt}=\frac{dR}{dx}*\frac{dx}{dt}\\ \frac{dR}{dt}=(1000-40x)*50\\ \text{When x=20}\\ \frac{dR}{dt}=(1000-40*20)*50\\ \frac{dR}{dt}=(1000-800)*50\\ \frac{dR}{dt}=10 \;000\\ \)

 

That is a daily rate. 

 Jul 19, 2019
 #6
avatar+102399 
+1

Sorry, Melody.....I was working on this at the same time......didnt mean to copy your answer  !!!

 

 

cool cool cool

CPhill  Jul 19, 2019
 #8
avatar+102774 
+1

I know that Chris,

Three answers are better than one anyway  laugh

Melody  Jul 19, 2019
 #5
avatar+102399 
+3

Revenue=  R  =  1000x - 20x^2

 

R  = 1000x  - 20x^2

 

dR/ dT  =  dR / dx *   dx / dT

 

So

 

dR / dT  =   (1000 - 40x ) *  [ 50 units per day ]

 

And when x  =  20

 

dR /dT  =  [1000  - 40 (20)] * [ 50]

 

dR /dT  =  [ 1000 - 800 ] * [50]

 

dR /dT    [ 200] * [50 ]  =   10,000

 

The revenue is changing by $10,000 when 20 units are sold

 

 

cool cool cool

 Jul 19, 2019

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