Algebra Discussion

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!

 A v e r a g e space equals fraction numerator t o t a l over denominator n u m b e r end fraction

Or in math speak,

x with bar on top equals fraction numerator capital sigma x over denominator n end fraction

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.

C left parenthesis m right parenthesis equals fraction numerator D e v i c e C o s t plus left parenthesis M o n t h l y B i l l right parenthesis m over denominator m end fraction

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?

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