To answer your questions:
1) The population growth from the year 2001 to 2007 is obtained by subtracting the population of 2001 from the population of 2007. In this instance, the population growth equates to 612.
2) Figuring out how long it took the population to grow from 1971 to 2583 students requires identify the years these population counts were reached and subtracting them. In this case, it took 6 years for the population to grow from 1971 to 2583 students.
3) The average population growth per year can be calculated by subtracting the population of the oldest year on record from the population of the most recent year, then dividing by the number of years. So, the average per year population growth is 95.
4) According to the data given, the population in the year 2000 was 1918 students.
5) Based on the assumption that the population increase is linear, we can find the linear equation which models population growth. To do this, we can calculate the slope 'm', which is the average population growth per year. The slope-intercept equation can then be expressed as P = mt + c, where 'c' is the y-intercept. Given that 'm' is 95 as calculated above, and that the y-intercept 'c' is given by the population of the year 2000 minus the product of the slope and the year 2000, we can calculate 'c'. Therefore, the equation for the population, P, of the school t years after 2000 is:
P = 95t + c
6) To predict the population in 2013, we simply substitute 2013 as 't' into the equation:
predicted_population_in_2013 = 95*2013 + c
And we get the predicted population in 2013 as 3153 students.