Q1: Do two different h enough. Take h=2,h=4

Model as shown in the picture below:

Model 1 (Exponential): find suitable a Model 2 (Logistic): find suitable a and K

1. As a Data Scientist at the National Institutes of Health (NIH), Ministry of Health, Malaysia. You are given a task to predict the growth of tumor for colon and rectum cancer. Develop suitable TWO (2) first order differential equation models to represent the growth of the tumor over time, t (in days). State all assumptions made to develop the model. By using THREE (3) numerical methods, approximate the growth of the tumor for 20 days. Simulate with three different step sizes. You can assume that, at the beginning the tumor size is 1 mm. Compare the results with analytical solutions. Discuss your finding and make decision on the best method for the prediction. Hint: [You can use Exponential and Logistic models). V(0) = V=1 mm3. = Model Name Differential Equation aV Exponential dy = a V Logistic dV dt dr =aV (1-) K