algebra

In most businesses, increasing prices of products can negatively impact the number of customers. The 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 approx. 40 customers per day for each $.25 increase in fare.

Let the number of riders be a function of the fares. Graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), and find the slope of the graph.

Hello jjwarren54!

Well, what do you think? Name the number of .25 increases \(\displaystyle x\). Let \(\displaystyle \,f(x)\,\)or\(\displaystyle \,y\,\) be the number of people.

Hence:\(\displaystyle \L \;\;f(x)\,=\,800\,-\,40x\,\,\Rightarrow\,y\,=\,-40x\,+\,800\).

Does that look like an equation of a line, parabola, hyperbola, or exponential ?

Hopefully I interpreted this problem correctly.

Thank you very much jonboy.

I believe this is a exponential. am i right?

It appears this is what they are getting at.

For every 25 cent increase they lose 40 customers.

Therefore, revenue would be:

\(\displaystyle \L\\R(x)=\overbrace{(2.25+0.25x)}^{\text{cost per rider}}\underbrace{(800-40x)}_{\text{number of riders}}=x^{2}-11x-180\)

where x = number of increases.

Hint: You should see this is not an exponential.

I suppose by the slope of the graph, they mean the derivative.