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September 17th, 2012, 07:43 AM   #1
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Renting a car

I have a tricky math question regarding renting car. I have to find a function that can describe the following situation.

A car rental agency charges a fee of 40$ for renting a car. The first 100 miles are for free, but after you exceed 100 miles, you have to start paying an extra 0.34$ per mile.

The key says the answer should be:

But if you drive say 50 miles, you only have to pay 23$, although the fee was 40$. The function above says that if you drive less than 100 miles, you will pay less then the 40$ start fee, which should not be possible.

The problem is to find a function that will give , When but when gives you the total amount you have to pay, 40$ fee + 0.34$/mile after 100 miles.

The function I'm looking for should be flat at 40$ the first 100 miles, but after 100 miles start to move up like a linear function. That is to say if you enter x=50 in the function you should get y=40$, and not 23$

All I get is this function below, although it is not complete. Their shoud be a flat line at 40$ the first 100 miles, and then move like the graph I have below. If you plot it you will see what I mean.



I'm really thankful if somebody could help me find this function.
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September 17th, 2012, 07:53 AM   #2
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Re: Renting a car

You could use a piecewise defined function:

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September 17th, 2012, 08:37 AM   #3
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Or y = 40 + .17(x - 100 + |x - 100|), for x ? 0.
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September 17th, 2012, 09:46 AM   #4
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Re: Renting a car

I'm greatful for your answers.

I was also thinking of a piecewise defined function, but I'm looking for one function that incorporates all x-values without making any definitions for the x-values and y-values.

The function I'm looking for should give a graph that lookes like the graph in the attached image file.

Is it even possible to make such a function?
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File Type: jpg renting car.jpg (12.8 KB, 111 views)
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September 17th, 2012, 09:54 AM   #5
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Re: Renting a car

[color=#008000]skipjack[/color] cleverly gave you such a function using absolute value.
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September 17th, 2012, 10:10 AM   #6
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Re: Renting a car

Oh sorry, I didn't really know what absolute values were, until you (MarkFl) pointed it out. I looked up what absolute values are about, and I now understand what skipjack meant.
One learns something new every day!

So once again I would like to thank skipjack and MarkFL for your answers.
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