Josephood7

 Solve the separable differential equation [math] Subject to the initial condition: [math].
[math] 

Consider the differential equation [math], where [math].
Find the solution to the differential equation when [math] in the form
[math]

 A tank, containing 1170 liters of liquid, has a brine solution entering at a constant rate of 5 liters per minute. The well-stirred solution leaves the tank at the same rate. The concentration within the tank is monitored and found to be

[math]

1. Determine the amount of salt initially present within the tank.
   
   Initial amount of salt =  kg
    
2. Determine the inflow concentration [math], where [math] denotes the concentration of salt in the brine solution flowing into the tank.
   
   [math]  kg / L

Initially 10 grams of salt are dissolved into 40 liters of water. Brine with concentration of salt 4 grams per liter is added at a rate of 4 liters per minute. The tank is well mixed and drained at 4 liters per minute.

1. Let [math] be the amount of salt, in grams, in the solution after [math] minutes have elapsed. Find a formula for the rate of change in the amount of salt, [math], in terms of the amount of salt in the solution [math].
   [math]  grams/minute
    
2. Find a formula for the amount of salt, in grams, after [math] minutes have elapsed.
   [math]  grams
    
3. How long must the process continue until there are exactly 20 grams of salt in the tank?
    minutes

 A country has 10 billion dollars in paper currency in circulation, and each day 75 million dollars comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the bank. Let [math] denote the number of new dollars in circulation after [math] days with units in billions and [math].

A. Determine a differential equation which describes the rate at which [math] is growing:
[math] 

B. Solve the differential equation subject to the initial conditions given above.
[math]

C. How many days will it take for the new bills to account for 90 percent of the currency in circulation?