A glass container can hold 35 liters of water. It currently has 10 liters of water with 15 grams of Gatorade power initially dissolved in the container. A solution is poured into the container at 3 liters per minute - the solution being poured in has 0.5 grams per liter of Gatorade powder. Assume the solution in the container is well mixed. There is an outflow at the bottom of the container which has liquid leaving at 1 liter per minute. Let G(t) denote the amount of Gatorade powder in the tank at time t.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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9. A glass container can hold 35 liters of water. It currently has 10 liters of water with 15 grams of
Gatorade power initially dissolved in the container. A solution is poured into the container at 3
liters per minute - the solution being poured in has 0.5 grams per liter of Gatorade powder.
Assume the solution in the container is well mixed. There is an outflow at the bottom of the
container which has liquid leaving at 1 liter per minute. Let G(t) denote the amount of Gatorade
powder in the tank at time t.
a. Setup the differential equation for G'(x).
b. Solve for the general solutiont)
c. Use initial condition to find the specific solution. (Write out the entire solution, with the
constant(s) plugged in.)
)
d. When will the container overflow?
Transcribed Image Text:9. A glass container can hold 35 liters of water. It currently has 10 liters of water with 15 grams of Gatorade power initially dissolved in the container. A solution is poured into the container at 3 liters per minute - the solution being poured in has 0.5 grams per liter of Gatorade powder. Assume the solution in the container is well mixed. There is an outflow at the bottom of the container which has liquid leaving at 1 liter per minute. Let G(t) denote the amount of Gatorade powder in the tank at time t. a. Setup the differential equation for G'(x). b. Solve for the general solutiont) c. Use initial condition to find the specific solution. (Write out the entire solution, with the constant(s) plugged in.) ) d. When will the container overflow?
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