SOLUTION: A tank of water is contaminated with 70 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

Question 1072367: A tank of water is contaminated with 70 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) Give a formula for S
- 70(81^t)
(b) 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?
- ??
(c) Suppose this cleanup procedure costs $8000 per hour to operate. How much does it cost to reduce the amount of salt from 70 pounds to 3 pounds? (Round your answer to the nearest dollar.
- ??
(d) How much does it cost to reduce the amount of salt from 3 pounds to 0.1 pound? (Round your answer to the nearest whole dollar.)
- ??

Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
At t(0) you have 70 lbs of salt in the tank. Since each hour of the process removes 19% of the salt solution, this leaves you with 81% of the salt you had to begin with. So the formula for the process would be:
a)Salt=70 lbs. x .81^t where t is the amount of time, in hours, that the process has been running.
b)To get down to 3 lbs of salt we need:
3=70 x .81^t
.81^t=70/3
t=approximately 14.95 hours
c)$8000/houe x 14.95 hours= $119584.95
d).1=3 x .81^t
t=16.41
$8000 x 16.41=$131280 to reduce the salt from 3 lbs. to .1 lbs.
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