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A rectangular field is to have an area of \( 500 \mathrm{~m}^{2} \). a. Write the perimeter, P, of the field as a function of the width, W. b. Find the domain of the function in part a. c. Use a graphing calculator to sketch the graph of the function in part a. d. Describe what the graph found in part c tells you about how the perimeter of the field varies with the width. a. The perimeter, \( P \), of the field as a function of the width, \( W \) is \( P(W)= \)