To create a linear model, we can use the formula for the equation of a line:
y = mx + b
where m is the slope and b is the y-intercept. We can calculate the slope using the formula:
m = (y2 - y1)/(x2 - x1)
Let's use the data from 1990 and 2005:
x1 = 1990, y1 = 210,000
x2 = 2005, y2 = 320,000
m = (320,000 - 210,000)/(2005 - 1990) = 11,000
Now we can use the point-slope form of a line to find the y-intercept:
y - y1 = m(x - x1)
y - 210,000 = 11,000(x - 1990)
y - 210,000 = 11,000x - 21,790,000
y = 11,000x - 21,580,000
So the linear model that predicts the population of Center City (y) in a given year (x) is:
y = 11,000x - 21,580,000
To find the year when the actual population of Center City was most different from the value predicted by this model, we can compare the actual population to the predicted population for each year and find the year with the largest difference.
Year | Actual Population | Predicted Population | Difference
1990 | 210,000 | 188,000 | 22,000
1995 | 240,000 | 239,000 | 1,000
2000 | 280,000 | 290,000 | 10,000
2005 | 320,000 | 341,000 | 21,000
We can see that the actual population was most different from the predicted population in 2005, with a difference of 21,000.