Chapter 4.2, Problem 16E

Reminder Round all answers to two decimal places unless otherwise indicated.

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 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 $S=S\left(t\right)$ 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?