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.

demandingwaffle Jul 19, 2019

#1**+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

ElectricPavlov Jul 19, 2019

edited by
Guest
Jul 19, 2019

edited by Guest Jul 19, 2019

edited by Guest Jul 19, 2019

#2**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.

demandingwaffle Jul 19, 2019

#3**+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.

Melody Jul 19, 2019

#5**+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

CPhill Jul 19, 2019