please help me figure out how to do this problem.?

Question

2) 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 1,000 per day. The bus company charges $2.00 for a ride. They conducted a survey of their customers and found that they will lose approximately 50 customers per day for each $.25 increase in fare.

a) Given the description above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), find the slope of the graph, find the price at which there will be no more riders, and find the maximum number of riders possible. The vertical axis is the number of riders per day, and the horizontal axis is the fare.

Graph:

Graph Type:

What is the slope of the graph?


b) The bus company has determined that even if they set the price very low, there is a maximum number of riders permitted each day. If the price is $0 (free), how many riders are permitted each day?

Answer 1

If the price is raised by p cents the number of riders is



(check: if raise $.25 they have 950; if raised $.50 they lose 100 - this checks)

This is the equation of a line.

Slope: -2
No more riders: p = 500 (so total price = 500 + 200 = 700)
Maximum number: if price is lowered by 200, the most they can do unless they pay people to ride, they have
1000 - 50*(-200) = 1400 riders.

Notice 2 things: first, this linear relationship will clearly not work at extreme cases (such as 0). Second, the choice of parameters will change these equations. For instance, if for p I used the price, instead of the change in price, the equation would be

r = 1000 - 50*(p - 200)/25

Both are right, as long as you explain clearly what p is.

Answer 2

well
if the price is $7.00, then 00 riders will be there
if the price is $0.00 , then maximum of 1400 riders will be there
morover the graph is a line (like that of negative acceleration)