The Gompertz differential equation N'it) = a\n-^Nit) serves as a model for the growth oftumors where A(/) is the number of cells in a tumor at time t. The maximum number of cells that can be supported is K, and a is constant related to the proliferative ability of the cells. In a particular type of cancer, a = 0.0439, k = 12000, and I is measured in months. At the time (f = 0) the tumor is detected, A(0) = 4000. Using the Adams predictor-corrector method with h = 0.5, find the number of months it takes for N(t) = 11000 cells, which is the lethal number of cells for this cancer

S343 Section 2.1 Notes- First Order Linear Equations and Integrating Factors 8-25-16 Recall equation for motion of falling object: = = − + o Position: = + + 2 0 0 o Velocity: = + 0 Replacing constants and with arbitrary functions of : = − + () o Arrive at general first order form + = ( )