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Stitz-Zeager_College_Algebra_e-book

# To solve x2 4x 6 0 we use x2 the quadratic formula and

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Unformatted text preview: plied domain for AC . 2. Find and interpret AC (10). 3. Solve AC (x) < 100 and interpret. 4. Determine the behavior of AC (x) as x → ∞ and interpret. Solution. ( 1. From AC (x) = C xx) , we obtain AC (x) = 80x+150 . The domain of C is x ≥ 0, but since x = 0 x causes problems for AC (x), we get our domain to be x > 0, or (0, ∞). 2. We ﬁnd AC (10) = per system. 80(10)+150 10 = 95, so the average cost to produce 10 game systems is \$95 3. Solving AC (x) < 100 means we solve 80x+150 x 80x + 150 x 80x + 150 − 100 x 80x + 150 − 100x x 150 − 20x x < 100. We proceed as in the previous example. < 100 <0 <0 common denominator <0 If we take the left hand side to be a rational function r(x), we need to keep in mind the the applied domain of the problem is x > 0. This means we consider only the positive half of the number line for our sign diagram. On (0, ∞), r is deﬁned everywhere so we need only look for zeros of r. Setting r(x) = 0 gives 150 − 20x = 0, so that x = 15 = 7.5. The test intervals 2 on our domain are (0, 7.5) and...
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