Question

These are differential equation problems. Pease show clear and legible work.

A 100 gallon tank is filled with a salt solution containing 10 lbs of salt. Pure water is pumped in at a rate of 5 gallons per minute and pumped out at the same rate. How many minutes will it take the amount of salt to drop to 2 lbs? Round to one decimal place. A 200 gallon tank initially has 100 gallons of a salt solution that contains 5 lbs of salt. A salt solution is pumped into the tank at a rate of 4 gallons per minute with a concentration of 1 lb of salt per gallon. The well-mixed solution is pumped out of the tank at a rate of 2 gallons per minute. How much salt will be in the tank after 35 minutes? Round to one decimal place. An object is removed from a room where the temperature is 71 degrees and is taken outside, where the air temperature is 29 degrees. After 1 minute, the temperature of the object reads 51 degrees. What will be the temperature of the object at t 2 minutes? (round your answer to two decimal places) -k (T- Ta) HINT: Use the equation dt The population in a town of 20,000 is growing by 15% per year. How long will it take the population to grow to 250,000? Round to the nearest year. Willmonite-35 is a newly found radioactive substance with a half life of 600 years. How much of 1,000 grams of Willmonite-35 will be left after 175 years? Round to the nearest gram. A 9.0-volt battery is connected to a series in which the inductance is 0.50 henry and the resistance is 8 ohms. Determine the current after 1 second if the initial current is di Ri = E(t) dt 0. Round to 2 decimal places. Hint: Use the model L

Answer 1

Y 5 rafe of salato Salt rate of salt Soluhon ton cenha un toogallun 5 X 5 gallnImi- IN purw Mpc Y 5 gallon Im 5 A 5 gallommin A 1H Out gven table ACcording t Dutlet Concentra rate of oulfton znlet (oncenhahin k rate intlow) Rate of Soluhun At - 5 A Integratingbt separatior Vanable A 5 dt el t to Ao A t Ln A-InAu- t 20 Ln A = t A (H=Ae h0 Guen at t=o Ao= tolb t20 plugging Vatues n obo ve fer AIL)- 2/b t/20 2= 10 e -t20 -t Ins) 20 -1.609 4 3 218 minute

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