A vat holds 100 cubic feet of liquid and is initially full. Liquid which is salt water with 1 gram of salt per 2 cu ft of liquid is being added at a rate of 2 cu ft per minute. It is mixed immediately, and the mixture is draining at 2 cu ft per minute, so the vat stays exactly full. Let y(t) denote the number of grams of salt in the vat at time t. Write the differential equation for y. Use the graphical method to plot two substantially different solutions for y, depending on the initial amount. Explain the difference. Then use the formula for solution of first-order linear DE to write the explicit solution if the vat is initially filled with pure water (i.e., no salt).