Cleaning contaminated water: A tank of water is contaminated with 60 pounds of salt. In order to bring the salt concentration down to a level consistent with EPA standards, clean water is being piped...

Cleaning contaminated water: A tank of water is contaminated with 60 pounds of salt. In order to bring the salt concentration down to a level consistent with EPA standards, clean water is being piped into the tank, and the well-mixed overflow is being collected for removal to a toxic-waste site. The result is that at the end of each hour there is 22% less salt in the tank than at the beginning of the hour. Let S = S(t) denote the number of pounds of salt in the tank t hours after the flushing process begins.

a. Explain why S is an exponential function and find its hourly decay factor.

b. Give a formula for S.

c. Make a graph of S that shows the flushing process during the first 15 hours, and describe in words how the salt removal process progresses.

d. In order to meet EPA standards, there can be no more than 3 pounds of salt in the tank. How long must the process continue before EPA standards are met?

e. Suppose this cleanup procedure costs $8000 per hour to operate. How much does it cost to reduce the amount of salt from 60 pounds to 3 pounds? How much does it cost to reduce the amount of salt from 3 pounds to 0.1 pound?