Consider a fish tank that initially contains 300 liters of water with 100 grams of salt dissolved in it. Water containing 4 grams of salt per liter is allowed to run into the tank at a rate of 2 liters per minute. The thoroughly stirred mixture in the tank is also allowed to drain out at a rate of 3 liters per minute.

(a) Find a differential equation for the amount of salt x(t) in the tank at time t.
(b) Solve the DE in (a).

Step-by-step explanation:

given that  a fish tank that initially contains 300 liters of water with 100 grams of salt dissolved in it. Water containing 4 grams of salt per liter is allowed to run into the tank at a rate of 2 liters per minute.

The thoroughly stirred mixture in the tank is also allowed to drain out at a rate of 3 liters per minute.

Let X(t) be the amount of salt in the tank at time t

X(0) = 100 gms.

Volume of tank at time t = initial volume+t(incoming rate-outgoing rate)

= 300+(2-3)t= 300 -t

Rate of change of X would be=incoming salt rate-outgoing salt rate

,X(0) = 100 gm

i.e.

this is linear DE

Solution woul dbe

Use initial condition to find t

X(0) = 100 = 1200+300^3C

C = -4.074(10^-5)

step-by-step explanation:

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