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 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. Show all work. Part B: If the newly constructed house requires 50 hours of work, how much will the interior designer earn? Show all necessary calculations. Part C: Determine an expression to represent the difference quotient for the function found in Part A. Show all necessary work.
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 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. Show all work.
Part B: If the newly constructed house requires 50 hours of work, how much will the interior designer earn? Show all necessary calculations.
Part C: Determine an expression to represent the difference quotient for the function found in Part A. Show all necessary work.
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