8. (12 points) Each of the following statements is false. Explain why or give a counterex- ample. (a) 23 dx = 0. (To see why it looks like this should be true, look at the graph of (b) It is always reasonable to assume the rate of growth of a population is proportional to its current size. (c) The solution of dy = y' is / y' dy = zy3 + C. (d) Suppose that the half life of a radioactive substance is five days, and we start with ten moles of it. Then ten days later it will have completely decayed