Students always ask, “When am I ever going to use this?” The following is a list of a few common math function types and associated real-world math contexts.

## Linear functions

**Anything that has a constant rate of change is a linear function.**

The total cost of bowling n games at a price of $5.00 per game when the shoe rental is $4.00:

A cell phone plan costs $59.99 for 1000 minutes. Additional minutes are $0.45 each. The monthly cost of the plan when you go over by x minutes:

Gasoline currently costs $3.799 per gallon. The cost of buying g gallons:

Degrees Fahrenheit and degrees Celsius are both used to measure temperature. Water freezes at 32 degrees Fahrenheit or 0 degrees Celsius. Water boils at 212 degrees Fahrenheit or 100 degrees Celsius. The temperature in degrees Fahrenheit when the temperature is c degrees Celsius:

## Exponential functions

**Anything with a constant percentage change is an exponential function.**

According to the Central Intelligence Agency, Argentina had a population of 41.8 million people in 2011 and was growing at a rate of 1.017% per year. The population of Argentina (in millions) t years since 2011:

According to the Central Intelligence Agency, Japan had a population of 126.4 million people in 2011 and was declining at a rate of 0.278% per year. The population of Japan (in millions) t years since 2011:

The future value of a $1000 investment earning 3.21% interest compounded monthly after t years:

## Piecewise functions

**Anything where different rules apply in different situations.**

The monthly cost of a cell phone plan with 1000 included minutes for $59.99 and extra minutes costing $0.45 when m total minutes are used:

The cost of n greeting cards when cards cost $1.29 each when 10 or less cards are ordered and cost $0.99 each when more than 10 cards are ordered: