When we say a function has a constant rate of change m, we mean that whenever input value changes the output value changes by m times as much. For example, Brunswick Kyrene Lanes in Chandler, Arizona, offered the following pricing for Monday through Friday daytime bowling in 2011.
Shoe rental: $4.25
Price per game: $3.49
In this context, the independent variable g represents the number of games played. The dependent variable C represents the total cost of playing g games (in dollars) including the cost of shoe rental. Since the price per game is $3.49 and does not change, we know the cost function has a constant rate of change of m = 3.49. We consider a table of values for the cost function.
Games Played g |
Cost (dollars) C |
1 |
3.49(1) + 4.25 = 7.74 |
2 |
3.49(2) + 4.25 = 11.23 |
3 |
3.49(3) + 4.25 = 14.72 |
4 |
3.49(4) + 4.25 = 18.21 |
Let’s verify that whenever the number of games increases the cost increases by 3.49 times as much.
In each of these cases, 3.49 times the change in the number of games equaled the change in cost.