Basic funtion, just can't figure out one part

1. Sep 17, 2006

Bitter

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?

2. Sep 17, 2006

vsage

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. Sep 17, 2006

Bitter

ah! Thank you. I feel stupid now. how could i overlook that.

4. Sep 27, 2006

Bitter

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. Sep 27, 2006

HallsofIvy

Staff Emeritus
Because x2+ 1 is never 0.