Determine the amount of salt in the tank at time t in Example 5 if the concentration of...

Determine the amount of salt in the tank at time t in Example 5 if the concentration of salt in the inflow is variable and given by lb/gal. Without actually graphing, conjecture what the solution curve of the IVP should look like. Then use a graphing utility to plot the graph of the solution on the interval [0, 300]. Repeat for the interval [0, 600] and compare your graph with that in Figure 3.1.4(a).

Reference: Figure 3.1.4(a), Example 5

Recall that the large tank considered in Section 1.3 held 300 gallons of a brine solution. Salt was entering and leaving the tank; a brine solution was being pumped into the tank at the rate of 3 gal/min; it mixed with the solution there, and then the mixture was pumped out at the rate of 3 gal/min. The concentration of the salt in the inflow, or solution entering, was 2 lb/gal, so salt was entering the tank at the rate R_in = (2 lb/gal) ⋅ (3 gal/min) = 6 lb/min and leaving the tank at the rate R_out = From this data and (5) we get equation (8) of Section 1.3. Let us pose the question: If 50 pounds of salt were dissolved initially in the 300 gallons, how much salt is in the tank after a long time?