Chapter 8: Problem 15
Water with a small salt content (5 lb in 1000 gal) is flowing into a very salty lake at the rate of \(4 \cdot 10^{5}\) gal per hr. The salty water is flowing out at the rate of \(10^{5}\) gal per hr. If at some time (say \(t=0\) ) the volume of the lake is \(10^{9}\) gal, and its salt content is \(10^{7}\) lb, find the salt content at time \(t\). Assume that the salt is mixed uniformly with the water in the lake at all times.
Short Answer
Step by step solution
Define the variables
Determine the rate of change of the volume
Express the volume as a function of time
Determine the rate of change of the salt content
Write the differential equation for S(t)
Solve the differential equation
Use initial conditions
Write the final solution
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Key Concepts
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