# algebra

#### jjwarren54

##### New member
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.

#### jonboy

##### Full Member
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.

#### jjwarren54

##### New member
Thank you very much jonboy.

I believe this is a exponential. am i right?

#### galactus

##### Super Moderator
Staff member
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.