During which time period did vermont's urban population increase the most? 1940 to 1950, 1950 to 1960, 1970 to 1980, 1980 to 1990

For this case the first thing you should do is to see the values of the domain and range of the function where there was a major change.
 We observe that for x = 1940 we have the value of y = 340.
 For x = 1950 we have the value of y = 470.
 The change was:
 470 - 340 = 130
 During this period there was the greatest growth of the population.
 
 Vermont's urban population increase the most in:
 1940 to 1950