```Question 80181
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.
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This problem has come up before with a few more questions attached. This the
response made a few weeks ago.
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Graph will be linear, (a constant change in x produces a constant change in y
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Let x = cost per person in dollars
Let y = number of riders
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Find the slope using the given coordinate: 2,1000
A 2nd coordinates could be 3, 800; (4 ea .25 increases reduces riders by 200)
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m = (800-1000)/(3-2) = -200, is the slope
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Find the equation using the point/slope equation:
y - 1000 = -200(x - 2)
y - 1000 = -200x + 400
y = -200x + 1400, our equation
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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( 300, 200, -2, 8, -500, 1500, -200x + 1400) }}}
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Graph Type: linear
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What is the slope of the graph? -200
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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?
This would occur when the fare is x=0:
y = -200(0) + 1400
y = 1400 riders when it's free (the y intercept)
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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?
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
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Both these situations can be seen on the graph, did this make sense to you?
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