9 gallons/hour entering with a salt concentration of 1/5(1+cos(t)) pounds/gallon (this is a function of time t).
15000 gallon capacity tank with 600 gallons of water with 5 pounds of salt dissolved inside.
6 gallons/hour leaving.
How much salt is the tank just before it overflows?
- salt concentration= 1/5(1+cos(t)) pounds/gallon (this is a function of time t)
therefore t=300 hrs when tank is full
Cin=1/5(1 + cost)
ds/dt=Rate in - rate out = CinRin - Cout*S(t)/V(t)
=1/5(1 + cost)*9 - 6*S(t)/(600+3t)
Solving the first order linear ODE we get: https://www.desmos.com/calculator/l7iixzgyll
therefore S(300)=279.797 Ib
does my solution look right?