My course is working on mixing problems and the practice sheet has several pieces for the same problem. I am confused about how to work this sort of problem and am looking to see one solved so I can have an idea of how to work them going forward. Would it be possible to see the steps worked for this problem?

Mixing problem

Rate in = 10 gallons per minute

Rate out = 10 gallons per minute

Concentration = 0.5 lbs per gallon

Initial Volume = 1000 gallons of fresh distilled water

Capacity volume = 1200 gallons

a.Find the volume rate of change in gallons per minute

b.Find the volume function, V(t) = mt + b. b = ?

c.Find the volume function, V(t) = mt + b. m = ?

d.Find the soluble amount inflow rate (pounds per minute)

e.Find the differential equation for the net rate of change of the soluble amount.

dtdy=a+by

What is the value of a?

f.Find the differential equation for the net rate of change of the soluble amount.

dtdy=a+by

What is the value of b?

g.Use the differential equation derived, find the coefficient of the term of the Taylor polynomial centered around zero. Assuming an initial amount of salt of 0 pounds (water in the tank at the beginning is distilled).

h.Find the solution for the differential equation for the net rate of change of the soluble amount. Assuming an initial amount of salt of 0 pounds (water in the tank at the beginning is distilled).

y=cert+b

What is the value of c? (in decimals)

i.Find the solution for the differential equation for the net rate of change of the soluble amount. Assuming an initial amount of salt of 0 pounds (water in the tank at the beginning is distilled).

y=cert+b

What is the value of r? (in decimals)

j.Find the solution for the differential equation for the net rate of change of the soluble amount. Assuming an initial amount of salt of 0 pounds (water in the tank at the beginning is distilled).

y=cert+b

What is the value of b?

k.Find the solution of the differential equation for the net rate of change of the soluble amount if the initial concentration of the tank is changed to 0.02 pounds of salt per gallon.

y=cert+b

What is the value of c?

l.Find the solution of the differential equation for the net rate of change of the soluble amount if the initial concentration of the tank is changed to 0.02 pounds of salt per gallon.

y=cert+b

Give the limit of y as time goes to infinity. (it is in pounds of salt)