A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 2 grams of salt per liter is then pumped into the tank at a rate of 4 L/min. The well-mixed solution is pumped out at a slower rate of 3 L/min. Write a differential equation that models the amount of salt in the tank at any time.

Salt flows in at a rate of

(2 g/L) * (4 L/min) = 8 g/min

and out at a rate of

(B/(200 + t) g/L) * (3 L/min) = 3B/(200 + t) g/min

where B is the amount of salt in the tank at time t.

Then the net rate at which B changes is governed by the ODE,

Multipy both sides by :

Integrate both sides:

The tank starts with 30 g of salt, so B(0) = 30, which gives

5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10

step-by-step explanation:

the true statements are:

r = set of real numbers

n = set of natural numbers, 1,2,

w = n u{0} = {0,1,}