Lab 05 Expectations

Submit Plots: 5
t=23 corresponds to the year 2020.

1. Plot actual data, this will be printed in number 5.
2. Find unique solution to (*) using P(0)=379 and P(1)=423, SHOW YOUR WORK. Predict population in 2020.
3. Find unique solution to (**), SHOW YOUR WORK. Predict population in 2020.
4. Approximate values of k and r, using h=10, the step size for 10 years. Then state the differential equation with the values you found. Predict the population in 2020 using (C). Please note that the P_0, P_1, and P_2 are for P(0), P(10), and P(20) respectively, since the step size is 10 years. Also both ways of calculating k should come out to be the same, so there is no need for averaging. K should be around 7994.
5. Graph all three equations on the same screen as #1 (3 estimates and 1 actual). Print this, and label each equation on plot. Which equation seems to be the most accurate? How much faith do you have in your predictions?
6. Measure the error approximation for each model. Do these values support your empirical observations? Explain.
7. Solve initial value problem (**) using this change. Discuss accuracy and predict population in 2020.
8. Show that P=0 and P=K are equilibrium solutions to (***). Draw rough picture of the phase plane. According to your work in #4 (and possibly the graph in #5), what will be the max population of NY?