The sell-by dating on dairy products depends on the solution of a differential equation. The rate of growth of bacteria in such products increases with time. If y is the number of bacteria (in thousands) present at time t and we have the differential equation dy (in days), then the rate of growth of bacteria can be expressed as ' dt shown below, where k is an appropriate constant. For a certain product, k = 4 and y = 48 (in thousands) when t = 0. Answer parts (a) and (b). dy = kt dt (a) Solve the differential equation for y. y= (Simplify your answer. Do not factor.)