how do i work this problem?

Calculus
Tutor: None Selected Time limit: 1 Day

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. 

Jul 11th, 2015

I'm so glad I could help you!

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.

Example:

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


Plot:

piecewise.png 


If you have any additional questions feel free to ask. If I made a silly error feel free to let me know.
Jul 11th, 2015

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