SOLUTION: I messed up and didn't send the whole problem, Please help!! In most businesses, increasing prices of their product can have a negative effect on the number of customers of the b

Click here to see ALL problems on Functions

Question 35301: I messed up and didn't send the whole problem, Please help!!
In most businesses, increasing prices of their product can have a negative effect on the number of customers of the business. A bus company in a small town has an average number of riders of 800 per day. The bus company charges $2.25 for a ride. They conducted a survey of their customers and found that they will lose approximately 40 customers per day for each $.25 increase in fare.
Given the description above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph you have drawn, and also the domain and range of the entire function excluding unrealistic values.
Answer by rapaljer(4671) (Show Source):
You can put this solution on YOUR website!
I am assuming that you are looking for an equation for Revenue.
Let x = number of $.25 price increases that the company has.

Number of riders = 800-40x
Cost to ride = $2.25 + .25x

The total revenue will be the number of riders times the cost per ride on the bus.

This is a parabola that opens down. Remember that x is the number of price increases, and R is the total amount of money --revenue-- that is taken in by the company. It is possible that a negative number of increases --lowering the price-- could add to the revenue, so x could be negative. Here is the graph

This graph is a result of trial and error with a LOT of different windows on the calculator.

R^2 at SCC