An interior designer wants to decorate a newly constructed house. The function f(x) = 49x2 - 200 represents the amount of money he earns per room decorated, where x represents the number of rooms he designs. The function (x) - = 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)

Part C: Determine an expression to represent the difference quotient for the function found in Part A. Show all necessary work. (5 points)