Question

Initially 10 grams of salt are dissolved into 35 liters of water. Brine with concentration of salt 4 grams per liter is added at a rate of 5 liters per minute. The tank is well mixed and drained at 5 liters per minute.

A.Let x be the amount of salt, in grams, in the solution after t minutes have elapsed. Find a formula for the rate of change in the amount of salt, dx/dt, in terms of the amount of salt in the solution x.
dxdt= grams/minute

B. Find a formula for the amount of salt, in grams, after t minutes have elapsed.
x(t)= grams

C. How long must the process continue until there are exactly 20 grams of salt in the tank?

minutes

Answer 1

(A)

Firstly, we will set up differential equation

(B)

now, we can sue variable seperable method

we can integrate both sides

now, we can take exponent

now, we have

at t=0, x=10

now, we can plug it back

(C)

we can set

x(t)=20

and then we can solve for t

...........Answer