SOLUTION: Could you please help me solve this question. I did some of it. Thank you It is not from a textbook, sorry. 2) In most businesses, increasing prices of their product can have

Question 82741: Could you please help me solve this question. I did some of it. Thank you
It is not from a textbook, sorry.
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:
c) If the bus company sets the price too high, no one will be willing to ride the bus. Beginning at what ticket price will no one be willing to ride the bus?
Answer: $7.00 per ticket

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
This same problem came up a few weeks ago, here is a solution that I submitted then.
:
:
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.
:
Graph will be linear, (a constant change in x produces a constant change in y
:
Let x = cost per person in dollars
Let y = number of riders
:
Find the slope using the given coordinate: 2,1000
A 2nd coordinates could be 3, 800; (4 ea .25 increases reduces riders by 200)
:
m = (800-1000)/(3-2) = -200, is the slope
:
Find the equation using the point/slope equation:
y - 1000 = -200(x - 2)
y - 1000 = -200x + 400
y = -200x + 1400, our equation
;
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: linear
:
What is the slope of the graph? -200
:
:
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:
This would occur when the fare is x=0:
y = -200(0) + 1400
y = 1400 riders when it's free (the y intercept)
:
c) If the bus company sets the price too high, no one will be willing to ride the bus. Beginning at what ticket price will no one be willing to ride the bus?
Answer:
This would be the x intercept, y = 0
-200x + 1400 = 0
-200x = -1400
x = -1400/-200
x = $7 fare will reduce the passengers to 0
:
Both these situations can be seen on the graph, did this make sense to you?

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