Question 611629
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Let *[tex \Large x] represent the number of videos rented.  Let *[tex \Large C_1] represent the cost of renting from club 1 and *[tex \Large C_2] represent the cost of renting from club 2.


The cost of renting from club 1 as a function of the number of videos rented is then:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C_1(x)\ =\ 2.5x\ +\ 25]


And the cost of renting from club 2 as a function of the number of videos rented is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C_2(x)\ =\ 3.25x]


The breakeven point is when the two functions are equal, so set them equal to each other and solve for *[tex \Large x].  If you get a non-integer answer, round up to the next whole number considering the sense of the question ("more economical").


Evaluate each function at your answer and verify that club 1 is indeed less expensive at this number of videos rented, then evaluate each function at your answer minus 1 and verify that club 2 is still less expensive at this point.  If you can answer yes in both situations, then you have done the problem correctly.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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