The Gompertz population model was described in Exercise 26 ofSection 2.3. The population is given by P{t) = PLe-ce ~ k ' where Pi, c, and A: > 0 are constants and P{t) isthe population attime t. P(t) satisfies the differential equation P'(t) = k fin PL - In P{t)] P{t). a. Using / = 0 as 1960 and the data given in the table on page 103, approximate Pi, c, and k. b. Apply the Extrapolation method with TOL I to the differential equation to approximate / , (1990), / > (2000), and / , (2010). c. Compare the approximationsto the values ofthe Gompertz function and to the actual population.

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