SOLUTION: A 40 gallon barrel is filled completely with pure water. Salt water with concentration of 0.4lb/gal is the pumped into the barrel, and the resulting mixture overflows at the same r

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Question 720800: A 40 gallon barrel is filled completely with pure water. Salt water with concentration of 0.4lb/gal is the pumped into the barrel, and the resulting mixture overflows at the same rate. The amount of salt in the barrel at time T is given by:

Q(T)=18(1-e^-0.06T)
where T is measured in minutes and Q(t) is measured in pounds.


A.)How much salt is in the barrel after 5 minutes?
B.)How much salt is in the barrel after 12.5 minutes?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+Q%28t%29+=+18%2A%28+1+-+e%5E%28-.06t%29+%29
+Q%28t%29+ is in pounds
+t+ is in minutes
(a)
+Q%285%29+=+18%2A%28+1+-+e%5E%28-.06%2A5%29+%29
+Q%285%29+=+18%2A%28+1+-+e%5E%28-.3%29+%29
+Q%285%29+=+18+-+18%2Ae%5E%28-.3%29+
+Q%285%29+=+18+-+18+%2F+e%5E.3+
+Q%285%29+=+18+-+18+%2F+1.3499+
+Q%285%29+=+18+-+13.3347+
+Q%285%29+=+4.6653+ pounds
(b)
+Q%2812.5%29+=+18+-+18%2Fe%5E.75+
+Q%2812.5%29+=+18+-+18%2F2.117+
+Q%2812.5%29+=+18+-+8.5026+
+Q%2812.5%29+=+9.4974+ pounds
Here's a plot of this function:
+graph%28+400%2C+400%2C+-4%2C+16%2C+-4%2C+16%2C+18%2A%28+1+-+e%5E%28-.06x%29%29+%29+