Let's go through the scenario step-by-step to formulate the function that describes Owen's payment to Ron for shoveling the driveway:
1. Flat Fee Payment (Initial Payment):
Owen pays an upfront flat fee of [tex]\( \$30 \)[/tex]. This is a one-time payment, independent of the number of months.
2. Monthly Payment:
After the initial payment, Owen continues to pay [tex]\( \$20 \)[/tex] for each month that follows.
To write down the function, let's define:
- [tex]\( y \)[/tex] as the total amount of money Owen pays.
- [tex]\( x \)[/tex] as the number of months.
The total cost [tex]\( y \)[/tex] will include:
- The flat fee of [tex]\( \$30 \)[/tex].
- An additional [tex]\( \$20 \)[/tex] for each month ([tex]\( x \)[/tex] months).
Therefore, the function that describes this situation can be written as:
[tex]\[ y = 30 + 20x \][/tex]
Where:
- [tex]\( 30 \)[/tex] represents the flat fee (initial payment).
- [tex]\( 20x \)[/tex] represents the recurring monthly payments (where [tex]\( x \)[/tex] is the number of months).
So, the completed function is:
[tex]\[ y = 30 + 20x \][/tex]
This equation describes the total amount Owen pays in terms of the number of months [tex]\( x \)[/tex].
