A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved. Brine containing 1 2 pound of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank after 15 minutes. (Round your answer to two decimal places.

47.25 pounds

Step-by-step explanation:

First, we determine the Rate In

Rate In=(concentration of salt in inflow)(input rate of brine)

Change In Volume of the tank,

Therefore, after t minutes, the volume of fluid in the tank will be: 100+2t

Rate Out

Rate Out=(concentration of salt in outflow)(output rate of brine)

Therefore:

This is a linear differential equation in standard form, therefore the integrating factor:

Multiplying the DE by the integrating factor, we have:

Initially, 20 pounds of salt was dissolved in the tank, therefore: A(0)=20

Therefore, the amount of salt in the tank at any time t is:

After 15 minutes, the amount of salt in the tank is:

a - base

b - exponent

so,