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**Week 6 Discussion**

Rational functions can show up in surprising places. For example, when you are finding the average, you are actually using a rational function!

Or in math speak,

Often when making an expensive purchase we look at the total cost and whether we are willing to pay it. Another way to consider this is to find the average cost per month to see if it is in your budget.

A common example would be when you renew the contract on your cell phone. Often we buy a new phone at the same time, and you can either pay it up front or have it added to your monthly bill.

If you pay for the device up front, you can use the following function to model the monthly cost, where m is the number of months you plan on owning the device.

Do some research to find the cost of a device you want to buy, and either your actual monthly bill or an advertised monthly bill. Using these numbers, give us the function you would use to model the monthly cost.

Based on the asymptotes, what would be the minimum monthly average cost for this phone and plan? Explain how you got your answer.

What would be the average cost if you replace the phone after 2 years (24 months)? Does this make you reconsider the price of the phones you buy?

Compare your classmates’ functions to your own. Do you think it’s the cost of the phone or the monthly cost of the phone plan that makes the most difference?

View your discussion rubric.

**respond to each question separately**

1. Jacob Gary

The device I want to get is an iPhone XS Max. The retail price for the 256gb one is $1300, and ill be doing a 30-month installment plan.

C(m)=

With the information I have, I can determine the minimum average cost would be about $85. I got my answer by using the equation.

If I were to replace my phone after 24 months the cost would hop to $95.83=$95.80. Yes, I think its better if you just save up for the phone and purchase it for $1300 instead of doing payments that’ll cost more at the end.

2.

I chose the Apple iPhoneXS Max. The full price is $1099.99 or it can be split over 24 months at $45.88 per month. I pay $65 for my monthly plan with no device fees.

The monthly cost for the bill with the device added on would be $110.83 which is $45.83 more per month than I currently pay. It is really the same cost either way it’s just a matter of paying up front in one lump sum or splitting it out over 2 years. If I had the money available, I would choose to purchase the phone outright instead of increasing my monthly bill. I don’t replace my phone until I have to so I will be using my iPhone 6s for as long as I can until I have to upgrade.