Answer:
13.57 kg
Step-by-step explanation:
Let the amount of salt in a tank be =[tex]\frac{salt in the tank}{volume of salt in the tank}[/tex]
= [tex]\frac{15}{50}[/tex]
= 0.3 kg/L
The concentration of salt coming into the tank = 0.333kg/L
We know that the concentration of salt leaving the tank should be:
amount of salt in the tank/volume of tank = y(t)/50 L
rate of change of salt = rate in - rate out
[tex]\frac{dy}{dt}[/tex] = 0.66 - [tex]\frac{y}{50}[/tex]
solving the differential equation gives :
ln y = 0.66/y (t) - 0.02 t + C
Initial conditions, t= 0; y (0) = 15
then ln 15 = C
ln y = [tex]\frac{0.66}{y}[/tex]t - 0.02t + ln 15
ln[tex]\frac{y}{15}[/tex] = 0.02t
y = 15e( exp -0.02t)
the amount of salt in 5 mins will be:
y (t) = 15e(exp -0.02 (5)
= 13.57 kg
