Writing Project 9:

Composition of piecewise defined functions

A travelling salesman in car insurances gets $1000 per month, plus $40 for every insurance he sells during the month. If he sells more than 50 insurances per month, he gets an additional bonus of $200. Express the income before tax of the salesman as a (piecewise defined) function of the number of contracts sold during the month.

Now the income tax function in this state is also piecewise defined. People making less than $700 during the month don't have to pay taxes. People who make between $700 and $2499.99 pay 10% of the income as tax. People who make between $2500 and $4000 pay 20%. People who make more than $4000 pay 30%.

Express the income after tax of the salesman as a (piecewise define) function of the number of contracts sold during the month.

Erich Prisner, August 2003