An interior designer wants to decorate a newly constructed house. The function $f(x) = 49x^2 - 200$ represents the amount of money he earns per room decorated, where $x$ represents the number of rooms he designs. The function $g(x) = \frac{1}{7}x$ represents the number of rooms the interior designer decorates, where $x$ is the number of hours he works. Part A: Determine the amount of money the interior designer will make decorating the house as a function of hours he works. (5 points) Part B: If the newly constructed house requires 50 hours of work, how much will the interior designer earn? Show all necessary calculations. (5 points)
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So, the function for the amount of money earned (M) as a function of the number of hours worked (h(X)) is: M(h(X)) = f(K) * g(X) Since the function f(K) = 497 - 200, we can substitute it into the equation: M(h(X)) = (497 - 200) * g(X) Simplifying Show more…
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