How do you know if this is exponential or linear?

Question

Johnny earns $25 each weekend for mowing his neighbor’s yard. He saves this money in a jar and

stores it under his bed. What type of function would represent how much money Johnny has in his jar

(assuming he doesn’t spend any of it)?

Answer 1

In the case of an exponential function, the amount of money he has would have to influence the amount of money he makes. For example in a savings account, the more money you have in it, the more interest you'll get (you'd get more interest on a million dollars than a hundred dollars). Thus, it would grow exponentially.

In the case of a linear function, the amount of money he has would be directly proportional to some other factor, not the amount of money he has.

In this case, the amount of money he earns is directly proportional to the number of weekends he works. If he works 1 weekend, he gets $25, 2 weekends will get him $50, 3 weekends gets him $75, and so on. If we were to plot these on a graph, we would see a straight line. So this case is a linear relationship.

Answer 2

He saves $25 per weekend. This represents a linear function, because the rate of change (slope) is constant.