Example: A tank initially contains 800 gallons of fresh water. Water containing 1/2 lb/gal of salt flows into the tank with the rate 6 gal/min and the well stirred mixture flows out at the rate of 2 gal/min. Write the initial value problem for Q(t), the amount of salt in pounds in the tank.

Q: vimming pool whose volume is 10,000 gal contains water that is 0.01% chlorine. Starting at t=0, city…

A: The solution is given by

Q: A large tank contains 50 gallons of water into which 5 pounds of salt has been dissolved. A solution…

A:

Q: A tank has initially 10 lb of salt dissolved in 100 gal of water. A solution containing a variable…

A:

Q: A tank originally contains 500 gallons of pure water. Brine containing 2 lb of salt per gallon is…

A:

Q: A culture of yeast grows at a rate proportional to its size. If the initial population is 9000 cells…

A: Introduction: When population grows at an exponential rate the general form of the exponential…

Q: A large tank is filled to capacity with 300 gallons of pure water. Brine containing 4 pounds of salt…

A: Tank has been filled to capacity with 300 gallons of pure water. Incoming rate of brine solution  is…

Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

A:

Q: A tank contains 240 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram…

A:

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.