As an example consider Activity 1 (and there are two other Activities).
At time t = 0 a tank contains Q(0) = 4$ lb of salt dissolved in 100 gal of water. Water containing 0.25 lb of salt per gallon is entering the tank at a rate of 3 gal/min, and the well-stirred solution leaves the tank at the same rate.
[a)] Build a differential equation for the amount of salt, $Q(t)$, in lb in the tank at time t in min. Hint: Keep track of the amount of salt that enters and exits the tank per minute.
[b)] Find an expression for the amount of salt, Q(t), in lb in the tank at time t in min and plot Q(t) vs. t over time interval [0, 200] min.
[c)] Determine when the amount of salt doubles from the original amount in the tank.
[d)] Determine when the amount of salt in the tank is 20 lb.
[e)] Determine when the amount of salt in the tank is 30 lb.
[f)] Determine the maximum amount of salt in the tank and when it occurs.
[g)] Describe the long term behavior of the amount of salt in the tank using accompanying plots to support your description.