How Is the Revenue Function R(x) = 500x(30-x) Derived for the Cable Firm?

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In summary, the conversation discusses the revenue function of a cable television firm, which is determined by the total monthly charge and number of customers. The function is represented by R(x) = 500x(30-x), where 30 is the given information and represents the maximum monthly fee that would result in 0 households with the service. The conversation also briefly touches on a question about a mathematical function. The answer is that the function does not have a hole in the graph because the common factor, x^2 + 1, is never equal to 0.
  • #1
Bitter
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The problem is this

A cable television firm presently serves 5000 households and charrges 20 dollars per month. A marketing survey indicates that each decrease of 1 dollar in the monthly charge will result in 500 new customers. Let R(x) denote the total monthly revenue when the monthly charge is x dollars.

Determine the revenue function R

The back of the book says
R(x)=500x(30-x)

I don't see where the 30 comes from, can anyone tell me?
 
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  • #2
30 is given information. It is obtained by observing that increasing the monthly fee by 10 dollars from 20 would result in 0 households with the service.
 
  • #3
ah! Thank you. I feel stupid now. how could i overlook that.
 
  • #4
Well, since my new problem relates to basic functions, I figured I'll just reuse to this topic.

This isn't exactly homework, but I just have a question.

Why does (x^2+1)(x-1)/(x^2 + 1)(x-2) not have a hole in the graph despite having a common factor?
 
  • #5
Because x2+ 1 is never 0.
 

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