Question

Identify the independent and dependent variables. Enter a function in function notation for the situation. Then use the function to solve the problem.

Stan, a local delivery driver, is paid $4.50 per mile driven plus a daily amount of $95. On Monday, he is assigned a route that is 40 miles long. How much is he being paid for that day?
The dependent variable is the ___________.
The independent variable is the ___________.
Let m represent the number of miles. Then, f(m) =___.
Stan is paid $___ for driving 40 miles that day.

Answer 1

The independent variable is the number of miles driven, and the dependent variable is the total amount paid. The function notation for Stan's pay is f(m) = 4.50m + 95. For a 40 mile route, Stan is paid $275 for the day.

Step-by-step explanation:

In this scenario, the independent variable is the number of miles driven (m), because this is the value that Stan can control and change. The dependent variable is the total amount Stan is paid (f(m)), as it depends on the number of miles he drives.

To express the situation in function notation, we take into account the $4.50 per mile and the daily amount of $95. Hence, the function can be written as f(m) = 4.50m + 95. Now, using the function to calculate how much Stan is paid for driving 40 miles on Monday, we substitute m with 40 to get f(40) = 4.50(40) + 95, which equals $275.