# Mixing Salt in Water in One Tank

Mixing Salt in Water in One Tank

This example comes from [1], Section 2.2, Modeling with First Order Equations.

The equation is

dQ(t)

dt

rQ(t)

100

r

4

where is time in minutes, is the amount of salt in the tank at time , is the rate of flow in and out of tank in gallons per minute. At time the tank contains pounds of salt in a tank containing 100 gallons of water. Assume that the tank is well stirred. In this example the mixture flowing into the tank contains 1/4 pound of salt per gallon, so one would expect that the tank will eventually contain 25 pounds of salt.

t

Q(t)

t

r=3

t=0

Q

0

Dragging the locator on the right changes the initial amount of salt found in the tank.

More than 1/4 pound of salt per gallon is colored dark orange or brown while less than 1/4 pound per gallon is colored dark green.