A solution of hydrochloric acid accidentally leaks into a spring fed freshwater lake, which in turn...

A solution of hydrochloric acid accidentally leaks into a spring fed freshwater lake, which in turn feeds a single stream. the acid leaks into the lake at a rate of 2 gallons per hour and has a concentration if 3 pounds per gallon. The lake initially contains 4000 gallons of water. Water flows into the lake from the spring at a rate of 100 gallons per hour and fluid flows out of the lake into the stream at a rate of 100 gallons per hour.
a) Set up the initial value problem that models the dynamics if acid in the lake.
b) Solve the initial value problem from part a.
c) compute the amount of acid in the lake after 1 hour

Expert Solution

Given that

the lake at a rate of 2 gallons per hour and has a concentration if 3 pounds per gallon

The lake initially contains 4000 gallons of water

Water flows into the lake from the spring at a rate of 100 gallons per hour

fluid flows out of the lake into the stream at a rate of 100 gallons per hour.

Colby Messinger answered 2 years ago

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