# Function solutions

This week we are learning about rational functions, and the discussion this week shows how you can use a rational function to determine how much your monthly phone bill will be.

These days when you get a new contract you have the choice to pay the phone up front, or to pay for it over the course of your contract. The total you pay for 2 years depends on which method you choose.

Pay up front: Total = phone + (monthly bill)(24)

How does the phone company figure out how much you’d pay monthly if you do it in installments? Well they do the following:

Pay in monthly installments = Total/24

We can generalize that equation to find the monthly bill as

If you plan on paying your phone off in 1 year, use m=12 (12 months) to find out how much you’d pay a month. If you want to pay it off after 2, pick m=24.

For this discussion you are to do the following:

1. Give the function C(m), doing research to determine numbers for the Device Cost and the Monthly Bill.
2. Find the asymptotes (horizontal and vertical)
3. Tell us what smallest monthly cost you can get the bill down to, and explain how you determined that.
4. Find out the average cost (i.e. the overall monthly bill) if you plan to pay the phone off in 2 years.
5. Reflect on this monthly cost. Does this make you reconsider the price of the phone you want to buy (i.e. maybe get a cheaper phone, or you have the money in your budget to spend more).