From Differential Equations, 4th Edition, by Paul Blanchard, Robert Devaney and Glen Hall

Lab 1.4

State: Montana

Year	Population
1850
1860
1870	21
1880	39
1890	143
1900	243
1910	376
1920	549
1930	538
1940	559
1950	591
1960	675
1970	694
1980	787
1990	799
2000	902

A. Using an exponential growth model, determine as accurate a prediction as possible for the population of your state in the year 2010. How much does your prediction differ from the prediction that comes from linear extrapolation using the populations in 1990 and 2000? To what extent do solutions of your model agree with historical data?

B. Produce a logistic growth model for the population of your state. What is the carrying capacity for your model? Using Euler's method, predict the population in the years 2010 and 2050. Using analytic techniques, obtain a formula for the population function P(t) that satisfies your model. To what extent do solutions of your model agree with historical data?

C. Comment on how much confidence you have in your predictions of the future populations. Discuss which model, exponential or logistic growth, is better for your data and why (if neither is very good, suggest alternatives).