Recall: we have a container into which we add a substance at a certain rate and remove the substance at another rate, then the rate of change of the amount of the substance in the container is given by the difference between the two rates. That is: rate of change = rate in rate out 4. Suppose that we are in the situation as in the last question of the previous worksheet: A tank of salt water has 100 pounds of salt dissolved in 1000 gallons of water, except that 2 pounds of salt but no water is added per minute. As before, 4 gallons of brine are pumped out each minute. (a) What will be the volume of liquid in the tank t minutes after the start? What will be the concentration of salt in the tank (in terms of S and t)? (b) Write down (but do not try to solve) an initial value problem for S (t) (c) How long can this situation continue for? (Hint: look at the denominator of your equation above!) (d) Use Euler's method in a spreadsheet to describe the behavior of 5(t) Pick a very small A2: to get good results. Model your solution until the maximum time you found above. Sketch a graph of S(t) below. (e) In practice, is this a good model for the entire time period? Why not? (Hint: think about solubility!)