A tank contains kg of salt and L of water. A solution of a concentration kg of salt per liter enters a tank at the rate L/min. The solution is mixed and drains from the tank at the same rate.
Find the amount of salt in the tank after hours.
You should know how to set up the differential equation that models this situation:
$\displaystyle \frac{dx}{dt} = (0.04)(8) - \left(\frac{x}{1000}\right) (8)$
where x is the amount (kg) of salt in the tank at time t. That is,
$\displaystyle \frac{dx}{dt} = \frac{40 - x}{125}$, subject to the boundary condition x = 80 when t = 0.
Solve the DE and hence solve for the value of x when t = 5.