Question 55501: 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:
Thanks for any help you may provide I don,t know how to graph this could you help please thank you tine
Answer by Hook(36)   (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=(y2-y1)/(x2-x1)
Here's what I get when I plug it in:
m = (760-800)/(2.5-2.25)
m = -40/.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+b
We know m, and we can plug in a point for x and y. Lets do that:
800 = -160(2.25)+b
Simplifying
800 = -360 +b
And adding 360 to both sides
1160 = b
Our line is y = -160x+1160
If we make the bus free (ie.. set x=0), how many people will ride? Let's see
y=-160(0)+1160
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 +1160
-1160 = -160x
7.25 = x
7.25 is the price that will cause nobody to ride the bus
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