An economy car rented in Florida from XYZ Rental on a weekly basis costs $95 per week. Extra days cost $24 per day until the day rate exceeds the weekly rate, in which the weekly applies. Also, any part of the day used counts as a full day. Find the cost, C, of renting an economy car as a function of the number of x days used, where 7<x<14. Graph the function.
This is a piecewise function meaning there isn't simply one function that represents the function. We already know the charge for one week ($95) is being charged because we have extended past 7 days.
We can identify within the range of the function 7<x<14 would cause the weekly price to apply by dividing the charge per week by the charge by day.
$95/$24 = 3.95 days. -> This means the maximum number of days you can be charged the daily fee for is 3. At 4 days, you have exceeded the cost of the weekly fee and will be charged $95.
1 week (7 days) - $95
1 week, 1 day (8 days) - $119
1 week, 2 days (9 days) - $143
1 week, 3 days (10 days) - $164
This is where the linear portion stops. Up to 1 week and 3 days (7<x<10) the function can be represented by C=24(x-7)+95.You must subtract the number of days that are charged based on the week before multiplying by the day rate. After this point, you would be charged for 2 weeks.
1 week, 4 days (11 days) - $190
1 week, 5 days (12 days) - $190
1 week, 6 days (13 days) - $190
1 week, 7 days (14 days) - $190
This portion of the plot (11<x<14) can be represented by C=190