The rate at which a solid substance dissolves [dQ/dt] varies directly as the product of undissolved solid present (in the solvent) [A - Q] and as the difference between the saturation concentration [Cs] and the instantaneous concentration [Ci] of the substance. Let Q -  the amount of the substance dissolved at any time t, Let A - the total amount of the substance, then dQ/dt = (A - Q)(Cs - Ci) Twenty pounds of salt is dumped into the tank containing 120 lb of solvent, and at the end of 22 minutes, the concentration is observed to be 1 part solute to 30 parts of solvent. Find the amount of solute that is in the solution at any time t, assuming that the saturation concentration is 1 part solute to 3 parts solvent.

Q: 2) A tank with capacity of 500 gallons initially holds 200 gallons of salt water containing 100 lb…

A: The capacity of the tank is 500 gallons initially holds 200 gallons of salt water containing 100 lb…

Q: A balloon leaks air (changes in volume) at a rate of one-third the volume per minute. Write an…

A: Given : A balloon leaks air (changes in volume) at a rate of one-third the volume per minute.

Q: Newton's law of cooling says that the temperature of a body changes at a rate proportional to the…

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Q: dM/dt=4M, M=25000 when t=2   dT/dx=-3.2T-1328, T=-212 when x=2

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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.