Originally Posted by

**MathBane** The question:

A tank of water is contaminated with 65 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 19% 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.1) Explain why *S* is an exponential function.

My answer: The amount of salt is being decreased by 19% each hour, so the decay is at a constant proportional rate.

(a.2) Find its hourly decay factor.

____

(b) Give a formula for *S*.

*S* =

(I thought this would be in a $\displaystyle a(b)^x$ format... but I'm not really sure at all.)