Question 88938: In most businesses, increasing prices of products can negatively impact the number of customers. 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.
a) Let the number of riders be a function of the fare charged. Graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), and find the slope of the graph.
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:
Show work in this space:
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:
Show work in this space:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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.
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a. Let the number of riders be a function of the fare charged. Graph the function, identify the graph of the function, and find the slope of the graph.
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Let x = cost of the bus ride; Let y = number of customers per day
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Lets say they increase the fare to $3 then the number of customers would be
800 - (3*40) = 680; x1 = 3; y1 = 680
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Lets say they increase the fare to $4 then the number of customers would be
800 - (7*40) = 520; x2 = 4; y2 = 520
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Find the slope using these coordinates:
m = (520 - 680)/(4 - 3) = -160 is the slope
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Find the equation using the point/slope equation: y - y1 = m(x - x1)
y - 680 = -160(x - 3)
y - 680 = -160x + 480
y = -160x + 480 + 680
y = -160x + 1160
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The graph should look like this:
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b. The bus company determined that even if they set the price very low, there are a maximum number of riders permitted each day. If the price is $0 (free), how many riders are permitted each day?
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You can see from the equation that when x = 0 (ride free), 1160 passengers would ride.
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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?
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That would be the x intercept, (y = 0)
-160x + 1160 = 0
-160x = -1160
x = -1160/-160
x = $7.25 would the fare when no one would be riding You can also see this on the graph
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A good check is to substitute the original fare for x, (2.25) and check to see
that y = 800
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How about this? Did it help you understand this problem?
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