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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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