1. The design life of a planned municipal water-distribution system is to end in 2050, and the population in the town has been measured every 10 years since 1930 by the US Census Bureau. The reported populations are given below. Year Population 1930 25521 1940 30208 1950 30721 1960 37253 1970 38302 1980 41983 1990 56451 2000 64109 Assuming the population growth follows the logistic curve pattern, a) Perform a non-linear regression to fit the historical data to the logistic curve equation, and estimate the populations in 2050 assuming four different scenarios where the Psat is 100, 110, 120 and 130 thousand people. Also determine coefficients a and b of the logistic model for each scenario.