Car Rental

[nycmath]

An economy car rented in Florida from Enterprise on a weekly basis costs 185 per week. Extra days cost 37 per day until the day rate exceeds the weekly rate, in which case the weekly rate applies. Also any part of a day used counts as a full day. Find the cost C of renting an economy car as a function of the number x of days used, where 7≤x≤14.

Let me see.

The base cost for 7 days (one week) is 185. This is given in the application. For extra days beyond 7 days, the cost per day is 37 dollars. This is also given.

The daily rate applies until the total cost goes above the weekly amount of 185 dollars. This is my understanding.

According to the question, we are in the second week (days 8 to 14). So, the cost is now the weekly rate plus the cost for extra days. Any part of the day counts as a full day. This is also given.

The ceiling function is [x - 7], which represents the number of extra days. For 7 less than x less than or equal to 14, the cost now is given by C(x) = 185 + 37[x - 7].

Stuck here........
Help....

Is this correct?

.

[Eigenvalue]

Yes, your function is correct.

[nycmath]

Yes, your function is correct.

I don't think that's the answer. I think the answer is a piecewise function but I could be wrong.

[Eigenvalue]

You did not mention another piece of the function; the piece you created a function for is correct. In technicality, your function is a piecewise function as it only pertains to the interval [7,14]