(4) Suppose you are trying to organize a rent strike in your apartment complex-that is, an effort to collectively withhold rent with your neighbors until your landlord, say, does something about the dangerous black mold in the apartments, instead of just painting over it. (Just an example.) The more tenants involved in the rent strike, the faster the strike grows; in your apartment complex of 200 tenants, the strike grows at a rate inversely proportional to the number of tenants not involved in the strike. (If you've never heard this terminology before: we say A is inversely proportional to B if A = _ for some constant k.) (a) Suppose your rent strike starts with just 2 people: you and your roommate. How many tenants are not involved in the strike when your organizing starts? (b) Write down a differential equation describing the rate of growth of your rent strike. (c) Solve your differential equation, using the initial condition from part (a). d) Suppose that one week later that is, after 7 days of organizing-you and your room- mate have convinced the 4 other tenants living on your floor to join the rent strike. When will half the tenants in the complex be participating in the strike? (5) You and several friends want to hang a banner from one of the overpasses in Davis to protest the UC Regents' new multi-year tuition increase (which is real, and not invented for this problem set). You decide to make your banner out of a piece of fabric shaped like an isosceles triangle, whose height is h yards and whose base is 2h yards. Your banner will be made from a heavy canvas, whose density is around 0.75 pounds per square yard. (a) Draw the banner. You may wish to label some relevant lengths. b) Draw and label a representative slice of your banner. Approximate its weight. c) Write down a definite integral which represents the total weight of the banner. If you're hanging the banner using a rope which can take exactly 50 pounds of weight, what are the maximum dimensions of the banner