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Graphing Word Problems

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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), 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?

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?

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?

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?

b) How far have you traveled after 4 hours?

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).

d) How far will you HAVE LEFT to travel to reach San Francisco after you have traveled 3 hours?

e) How far will you HAVE LEFT to travel to reach San Francisco after you have traveled 4 hours?

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).

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  • BSc , Wuhan Univ. China
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Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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