SOLUTION: The table represents the total cost an online store charges for streaming movies. It charges an annual membership fee and a fee for each movie streamed. Movies Streamed- 0,1,2,

Question 1117437: The table represents the total cost an online store charges for streaming movies. It charges an annual membership fee and a fee for each movie streamed.
Movies Streamed- 0,1,2,3
Total Cost- 52,55.40,58.80,62.20
A local rental store uses the function C=4.60m to determine how much to charge for movie rentals. C is the total cost and m is the number of movies rented. The store does not charge customers a membership fee. If 50 movies are rented in a year, which option is cheaper?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let

represent the cost function for streaming

movies, and let

represent the cost function for renting

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:

And we are given the rental cost function directly:

All that you need to do is to calculate

and

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

My calculator said it, I believe it, that settles it

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