Objectives: Solve a system of ODEs using built-in Matlab functions like ode45(). You must be able to setup the inputs properly by hand or in Matlab. The Lotka-Volterra predator-prey model uses first-order differential equations to estimate the populations of two interacting species, p₁ and p2- dpi dt dp2 dt = a*pi-ß* P1 * P2 Script = 8 * P1 * P2-Y * P2 where a is the prey's growth rate, ß is the prey's death rate, & is the predator's growth rate and y is the predator's death rate. We want to model the population of snow hares (pi) and Canadian lynxes (p2). Assume: ▪ the population at t=0 is 100 hares and 5 lynxes ▪ all rates are constant ▪ no other factors influence population size Your final script should: 1. implement the predator-prey model with a = 0.48, ß= 0.025, y = 0.68 and 8 = 0.02. 2. solve the system of differential equations at all timepoints in tYears = 0:0.25:100 using ode45 and the initial populations provided in po 3. assign the resulting population estimates to a 2-column matrix named ppPop. Prey should be in the first column and predator in the second Make sure you supply a time vector instead of a time span to the solver ensures the solutions are evaluated at the same time points for the grader tool. 1 pe = [100 5]; % population of snow hares, lynxes at t=0 2 tYears = 0:0.25:100; % discrete time interval, in years 4% Add your code below 6 % Model parameters (can be moved to where needed in your script) 7 a = 0.48; % prey's growth rate 8 b = 0.025; % prey's death rate 9 c = 0.68; % predator's death rate 10 d = 0.02; % predator's growth rate 11

Note: Round your final answer to 2 decimal places if it is not a whole number.   Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.

Answer the value of the integration constant C4. Enter your answer in kNm2 to three decimal places.

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