SOLUTION: 2) 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.

Algebra ->  Graphs -> SOLUTION: 2) 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.       Log On


   

Question 55028: 2) 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.
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), find the slope of the graph, find the price at which there will be no more riders, and the maximum number of riders possible.
Graph:
Graph Type

What is the slope of the graph?

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?
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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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3) It is approximately 480 miles from Los Angeles, California, to San Francisco, California. Allowing for various traffic conditions, a driver can average approximately 60 miles per hour.
a) How far have you traveled after 3 hours?
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b) How far have you traveled after 4 hours?
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c) How far have you traveled after t hours (i.e., write a linear function that expresses the distance traveled, d, as a function of time, t).
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d) How far will you HAVE LEFT to travel to reach San Francisco after you have traveled 3 hours?
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e) How far will you HAVE LEFT to travel to reach San Francisco after you have traveled 4 hours?
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f) How far will you HAVE LEFT to travel to reach San Francisco after you have traveled t hours (i.e., write a linear function that expresses the distance to be traveled to reach San Francisco, s, as a function of time, t).
Answer:
Answer by Hook(36) About Me  (Show Source):
You can put this solution on YOUR website!
You know right away that this is a line. Every $0.25 change in price means a change of 40 customers...a linear relationship. Besides, they ask for the slope...that's a characteristic of a line.
Let's find the slope. At $2.25, 800 customers ride the bus. At $2.50, 760 folks will ride the bus. Remember the formula for slope m=%28y2-y1%29%2F%28x2-x1%29
Here's what I get when I plug it in:
m+=+%28760-800%29%2F%282.5-2.25%29
m+=+-40%2F.25
m+=+-160
The slope of the line is -160 passengers per dollar.
Let's come up with an equation for our bus-rider line. In slope-intercept form, its y=mx%2Bb
We know m, and we can plug in a point for x and y. Lets do that:
800+=+-160%282.25%29%2Bb
Simplifying
800+=+-360+%2Bb
And adding 360 to both sides
1160+=+b
Our line is y+=+-160x%2B1160
If we make the bus free (ie.. set x=0), how many people will ride? Let's see
y=-160%280%29%2B1160
y+=+1160
1160 folks will ride the bus max.
Ok...what price will cause there to be no riders (ie...set y=0)?
0+=+-160x+%2B1160
-1160+=+-160x
7.25+=+x+
7.25 is the price that will cause nobody to ride the bus