Environmental Science: Water Purification (61 continued) a. Use a graphing calculato...

Environmental Science: Water Purification (61 continued)

a. Use a graphing calculator to graph the cost function C(x) from Exercise 61 on the window [50, 100] by [0, 20]. TRACE along the curve to see how rapidly costs increase for purity (x-coordinate) increasing from 50 to near 100.

b. To check your answers to Exercise 61, use the “dy/dx” or SLOPE feature of your calculator to find the slope of the cost curve at x = 95 and at x = 98. The resulting rates of change of the cost should agree with your answers to Exercise 61(b) and (c). Note that further purification becomes increasingly expensive at higher purity levels.

Environmental Science: Water Purification If the cost of purifying a gallon of water to a purity of x percent is

a. Find the instantaneous rate of change of the cost with respect to purity.

b. Evaluate this rate of change for a purity of 95% and interpret your answer.

c. Evaluate this rate of change for a purity of 98% and interpret your answer.