Question 70609: 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:
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:
3) It is approximately 300 miles from Chicago, Illinois, to St. Louis, Missouri. Allowing for various traffic conditions, a driver can average approximately 60 miles per hour.
a) How far have you traveled after 3 hours?
Answer:
Show work in this space:
b) How far have you traveled after 4 hours?
Answer:
Show work in this space:
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.
Answer:
d) How far will you HAVE LEFT to travel to reach St. Louis after you have traveled 3 hours?
Answer:
Show work in this space:
e) How far will you HAVE LEFT to travel to reach St. Louis after you have traveled 4 hours?
Answer:
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f) How far will you HAVE LEFT to travel to reach St. Louis after you have traveled t hours? i.e. write a linear function that expresses the distance to be traveled to reach St. Louis, s, as a function of time, t.
Answer:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! phs/70609 (2007-02-13 21:32:41): 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.
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Let x = cost(in $'s) of the ride; let y = the number of riders
:
It looks like a linear equation with a negative slope
Using the given data:
1000 passengers at: $2. At $1 increase: [1000 - 4(50)] = 800 passengers at $3
x1 = 2; y1 = 1000, x2 = 3, y2 = 800
:
Find the slope: m = (800-1000)/(3-2) = -200 is the slope
:
Using the point slope equation: y - y1 = m(x - x1)
y - 1000 = -200(x - 2)
y - 1000 = -200x + 400
y = -200x + 400 + 1000
y = -200x + 1400
:
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 is when x = 0, and is the y intercept which is 1400 passengers
as can be seen by the graph
:
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 occurs at the x intercept, when x = 7, hence a cost of $7 reduces passenger number to 0
:
:
3) It is approximately 300 miles from Chicago, Illinois, to St. Louis, Missouri. Allowing for various traffic conditions, a driver can average approximately 60 miles per hour.
a) How far have you traveled after 3 hours?
Answer:
Dist = time * speed, d = 3*60 = 180 mis
:
b) How far have you traveled after 4 hours?
Answer:
d = 4 * 60 = 240 mi
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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.
Answer: d = 60t
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d) How far will you HAVE LEFT to travel to reach St. Louis after you have traveled 3 hours?
Answer: d =
Show work in this space:
e) How far will you HAVE LEFT to travel to reach St. Louis after you have traveled 4 hours?
Answer: d = 300 - (4*60) = 60 mi
:
f) How far will you HAVE LEFT to travel to reach St. Louis after you have traveled t hours? i.e. write a linear function that expresses the distance to be traveled to reach St. Louis, s, as a function of time, t.
Answer: d = 300 - 60t
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