In lab 1 we consider the Gompertz equation for the population growth of cancer cells in a tumor, y' = ry ln(K/y). In this problem we investigate this further. (a) Find the linear (tangent line) approximation to the right-hand side of the differential equation that is valid near y = K . Using this, what is the linearization of the differential equation at y = K? (b) Solve the Gompertz equation and the linearization that you found in (a) exactly. (c) Note that we expect the linear approximation to be a good model for the original Gompertz equation when y is close to K. Your solution to the Gompertz equation should look like y = Kex , for some expression x. Find the Taylor expansion for ey around y = 0, and use this to write the Taylor expansion for your solution to the Gompertz equation. Show that when t is large this expansion is the same as the solution to the linearization of the equation.