A manufacturer of a chocolate beverage mixes liquid chocolate with milk in a large vat containing 450 liters of the mixture that is 20% chocolate initially. The differential equation for A, the amount of chocolate in the vat at time t, follows a "rate in - rate out" model. When chocolate flows in at a rate of 2 liters/min and the mixed beverage flows out at the same rate, you can model the situation with the differential equation liters/min which can be rewritten as .
a) What is the particular solution to this differential equation?
b) In the long run, how many liters of chocolate will be in the mixture contained in the vat?

Question

A manufacturer of a chocolate beverage mixes liquid chocolate with milk in a large vat containing 450 liters of the mixture that is 20% chocolate initially. The differential equation for A, the amount of chocolate in the vat at time t, follows a "rate in - rate out" model. When chocolate flows in at a rate of 2 liters/min and the mixed beverage flows out at the same rate, you can model the situation with the differential equation  liters/min which can be rewritten as  .
a) What is the particular solution to this differential equation?
b) In the long run, how many liters of chocolate will be in the mixture contained in the vat?

Quizplus · Accepted Answer

The Answer of A manufacturer of a chocolate beverage mixes liquid chocolate with milk in a large vat containing 450 liters of the mixture that is 20% chocolate initially. The differential equation for A, the amount of chocolate in the vat at time t, follows a "rate in - rate out" model. When chocolate flows in at a rate of 2 liters/min and the mixed beverage flows out at the same rate, you can model the situation with the differential equation  liters/min which can be rewritten as  .
a) What is the particular solution to this differential equation?
b) In the long run, how many liters of chocolate will be in the mixture contained in the vat?

A Manufacturer of a Chocolate Beverage Mixes Liquid Chocolate with Milk