When looking at a word problem and deciding whether it is linear or exponential you need to look at the rate of change.

Linear Contexts

If the rate of change is increasing or decreasing at a constant or steady rate, then you can conclude that the word problem would be best modeled by a linear function.

For example: If you keep your money in a piggy bank and add $2 to your bank every week, you are saving your money at a linear rate. Every week your money will grow by $2 regardless of the amount you have previously saved.

Exponential Contexts

If the rate of change is increasing or decreasing by a factor or percent, then you can conclude that the word problem would be best modeled by an exponential function.

For example: If you keep your money in a savings account with your local bank, you will collect interest. Banks set an interest rate that is given as a percent. Since there is a percent increase, you will not earn the same amount in interest every year. If you deposit $1000 into your account and do not take any money out or deposit any more, and the annual interest rate is 0.75%, you will earn $7.50 in interest in the first year (1000 x .0075 = 7.50). This leaves you with $1007.50 at the end of the first year. The next year you will earn $7.56 in interest (1007.50 x .0075 = 7.65), leaving you with $1015.06 at the end of the year. The year after that you will earn $7.61 (1015.06 x .0075 = 7.61). As you can see, the amount of change is increasing from 7.5 to 7.56 to 7.61. This amount of change each year will continue to increase.