Solve Question 24 and 25, question 23 is already solved on Bartleby 23. A large tank is filled to capacity with 500 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gal/min. The well- mixed solution is pumped out at the same rate. Find the number A(t) of pounds of salt in the tank at time t. 24. In Problem 23, what is the concentration c(t) of the salt in the tank at time t? At t = 5 min? What is the concen- %3D tration of the salt in the tank after a long time, that is, as t→ 00? At what time is the concentration of the salt in the tank equal to one-half this limiting value? 25. Solve Problem 23 under the assumption that the solu- tion is pumped out at a faster rate of 10 gal/min. When is the tank empty?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.