Bonus (20 pts) Bonus: Use solver fromAPI to get IVP # Answer from scipy.integrate import solve_ivp from math import pi as PI/nQuestion (30 pts) Use Runge-Kutta's method to solve and plot this better predator prey model by incorporating interaction terms. Lotka-Volterra equations dN dt =aN – BPN dP = SPN-P dt Where a is prey best case growth, ẞ prey growth dependent on predators, y worst case predator death, & predator growth dependent on prey. = Use: a = 2/3, 8 4/3, y = 8 = 1, P(0) = N(0) = 1.3 # Answer N = lambda n, p: a В p*n P = lambda n, p: 8 * p*n * - Y р/nQuestion (20 pts) Use Euler's method to solve and plot differential equations of a 3 way predator pray model (like rock paper scissors). In this case lets presume it is: bacteria kills person, virus kills bacteria, and person kills virus. Unrealistically, though... pretend that each killing the other means a victory and increases their population. Solve/plot for enough time points and dt size to show a trend. Person (P)/nHomework 06 Question (50 pts) Investigate Difficile data set. In this dataset patients are given a drug to help improve their energy. 1. You will first need to replace dose 0 with "placebo", 1 with "low", 2 with "high". 2. View grouped descriptive statistics. 3. Plot libido vs dose as a boxplot. 4. Plot libido vs dose as a bar chart with Cl. 5. Run 1-way ANOVA 6. Run a pairwise ANOVA to check for dose's significance on libido. Difficile data set source

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