The cost, in thousands of dollars, of airing x television commercials during a s

Question

The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 150 + 2,500x - 0.03x^2. (a) Find the marginal cost function C?(x). HINT [See Example 1.] C?(x) = 2500 - .06x Use it to determine how fast the cost is increasing when x = 4. 2499.76 thousand dollars Compare this with the exact cost of airing the fifth commercial. The cost is going up at the rate of $ 2499.76 per television commercial. The exact cost of airing the fifth commercial is $ 2499.73. Thus, there is a difference of $ 0.03.

Explanation / Answer

C(5) = 150 + 2500(5) - 0.03(5)^2

C(5) = 12649.25 --> cost of airing 5 commercials

C(4) = 150 + 2500(4) - 0.03(4)^2

C(4) = 10149.52 --> cost of airing 4 commercials

So, cost of the 5th commercial = C(5) - C(4)

12649.25 - 10149.52

2499.73 ---> EXACT COST

There is a difference of 0.03 dollars

Here is how we enter the answer :

Cost going up at a rate of $ 2499.76

Exact cost of airing the 5th comm = $ 2499.73

Difference is $0.03

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