Using MATLAB

2. Consider the following problem dealing with the "Gompertz equation", which is a simple model for tumor growth: a. Write a code to solve the system of ODEs listed in the top line (i.e., solve for N and ). Make clear what approach you took to solve the ODEs (e.g. RK4, ode45). Along with your code, include several plots to indicate the general dynamics of the tumor growth. b. Carry through the calculation as described in the "figure". That is, clear show how the system can be reduced to two different forms of a single 1st order ODE c. Modify your code from the first part to also independently solve these two other versions of the equations. Are they all equivalent? Show at least one plot comparing all three to argue your case, indicating/explaining any differences. A solid tumor usually grows at a declining rate because its interior has no access to oxygen and other necessary substances that the circulation sup- plies. This has been modeled empirically by the Gompertz growth law, dN dt yN where = dt is the effective tumor growth rate, which will decrease exponentially by this assumption. Show that equivalent ways of writing this are dN dt 2. Consider the following problem dealing with the "Gompertz equation", which is a simple model for tumor growth: a. Write a code to solve the system of ODEs listed in the top line (i.e., solve for N and ). Make clear what approach you took to solve the ODEs (e.g. RK4, ode45). Along with your code, include several plots to indicate the general dynamics of the tumor growth. b. Carry through the calculation as described in the "figure". That is, clear show how the system can be reduced to two different forms of a single 1st order ODE c. Modify your code from the first part to also independently solve these two other versions of the equations. Are they all equivalent? Show at least one plot comparing all three to argue your case, indicating/explaining any differences. A solid tumor usually grows at a declining rate because its interior has no access to oxygen and other necessary substances that the circulation sup- plies. This has been modeled empirically by the Gompertz growth law, dN dt yN where = dt is the effective tumor growth rate, which will decrease exponentially by this assumption. Show that equivalent ways of writing this are dN dt