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lab_05_notes

# lab_05_notes - required PROBLEM 6 Type that command to find...

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LAB #5 NOTES PROBLEM 1 Type in the MATLAB code as shown. Print off the graph. To highlight each datapoint, you could use the command: plot(T,A, ‘-*); PROBLEM 2 Solve the separable ODE ( r dt dP = ) using P(0)=379 and P(1) = 423. To predict the population in 2020, note that t = 0 is 1790 and t = 1 is 1800. Thus, the t that corresponds to 2020 is (2020 – 1790) / 10 = 23. PROBLEM 3 Repeat Problem 2 with the second seperable ODE ( rP dT dP = ). PROBLEM 4 Don’t derive this solution. Compute the value of r and the two values of K with h = 10 (h is the step-size, and as you can see, ours is every 10 years). Average the two values of K and use that in P(t) to find the population in 2020. PROBLEM 5 Plot the 3 solutions lines in MATLAB on top of the plot from Problem 1. You may want to use different shapes for the data points to differentiate one solution from the other, but this is not

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Unformatted text preview: required. PROBLEM 6 Type that command to find the ε-value between the solutions and the actual data. Be careful when using the notation. Save your solution to vector B and keep your data in vector A. PROBLEM 7 Using seed = 50, we now 1880 the new t = 0. Repeat Problem 3 using P(0)=995 and P(1)=1231. Find the population at 2020 as before and address the accuracy of this new solution line. PROBLEM 8 An equilibrium solution occurs when your solution is a constant. Therefore, the derivative of the solution is equal to zero. Because of this, to find the equilibrium solutions of a differential equation, you would set = dt dP and solve for the solutions. You may want to check the stability of K to show that regardless of whether the P(0) is above or below the value of K, the ending maximum population will always be K....
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lab_05_notes - required PROBLEM 6 Type that command to find...

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