The answer is we use the logarithm by denition log2 x

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Unformatted text preview: tal cost C of connecting the Junction Box to the Outpost as a function of x, the number of miles the cable is run along Route 117 before heading off road directly towards the Outpost. Determine a reasonable applied domain for the problem. 2. Use your calculator to graph y = C (x) on its domain. What is the minimum cost? How far along Route 117 should the cable be run before turning off of the road? Solution. 1. The cost is broken into two parts: the cost to run cable along Route 117 at $15 per mile, and the cost to run it off road at $20 per mile. Since x represents the miles of cable run along Route 117, the cost for that portion is 15x. From the diagram, we see that the number of miles the cable is run off road is z , so the cost of that portion is 20z . Hence, the total cost is C = 15x + 20z . Our next goal is to determine z as a function of x. The diagram suggests we can use the Pythagorean Theorem to get y 2 + 302 = z 2 . But we also see x + y = 50 so that y = 50 − x. Hence, z 2 = (50 − x)2 + 900. Solving for z , we...
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