Many organ pipes in old European churches are made of tin. In cold climates such pipes can be affected with tin pest, when the tin becomes brittle and crumbles into a gray powder. This transformation can appear to take place very suddenly because the presence of the gray powder encourages the reaction to proceed. In this exercise we assume the rate of the reaction is proportional to the product of the amount of tin left and the quantity of gray powder, p, present at time t. So that you can express the amount of tin left at any time, we also assume that when metallic tin is converted to gray powder the mass of tin plus the mass of grey matter remains equal to the quantity of tin initially present. (a) Write a differential equation for p. Let the constant B represent the quantity of tin initially present. (Use k>0 as the constant of proportionality.) (b) How much metallic tin has crumbled when it is crumbling fastest?