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141Bquiz7c - 1 MATH 141B Quiz#7 Due Tues More interesting...

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1 MATH 141B Quiz#7 Due: Tues March 18, 2008 More interesting and realistic models take some time to set up. However, since I’ve clearly laid things out, you’ll simply be going through the 7-step method to solve a linear differential equation, and taking a limit to get long range information. [ 2 ] 1. A 100-gallon is filled with pure water . Salt water (brine) of concentration 0.1 pounds of salt per gallon of water is pumped into the tank at 25 gallons per minute. Brine leaves the tank at the same rate. Let y ( t ) denote the amount of salt in the tank at time t . Set up and solve a first order differential equation for the unknown function y ( t ) and compute the amount of salt in the tank in the long run. That is, find y = lim t →∞ y ( t ) . In this problem, you will be using the differential equation y = - ( F V ) y + I. Note that I = c · F , as the units confirm: lbs gal · gal min = lbs min (since gallons cancel). A) y = 10, B) y = 15, C) y = 20, D) y = 25, E) none of the above [ 2 ] 2.
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