Question 1117437
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Let *[tex \Large C_s(m)] represent the cost function for streaming *[tex \Large m] movies, and let *[tex \Large C_r(m)] represent the cost function for renting *[tex \Large m] movies.


Since for streaming zero movies the cost is $52, $52 is clearly the amount of the annual fee.  Then one movie costs 55.40, so just the movie is 3.40.  Two movies are 58.80, so two movies are 6.80, or two times 3.40. The cost of three movies fits the pattern, so we are reasonably certain that the function is linear and that the slope is 3.40 while the y-intercept is 52, hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C_s(m)\ =\ 3.40m\ +\ 52]


And we are given the rental cost function directly:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C_r(m)\ =\ 4.60m]


All that you need to do is to calculate *[tex \Large C_s(50)] and *[tex \Large C_r(50)] and decide which is smaller.


Looking at the problem from an intuitive point of view, notice that if 52 movies were streamed, they would actually cost $4.40 each on an annualized basis, whereas the rentals are a fixed $4.60.  The question of which is cheaper at 50 movies rented should be obvious.


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