Part A: Use the data points (7, 15400) and (13, 22600) to write a linear model of the form: f(t) = mt + b, where t is the number of years after 2000 and b is the population in 2000.
f(t) = mt + b, where t is the time / number of years after 2000, m is the slope, and b is the y-intercept.
Let's call f(t) = f(x) = y and t = x.
m = (y2 - y1) / (x2 - x1), where (x1, y1) = (7, 15400), the 1st set of x and y values, and (x2, y2) = (13, 22600) is the 2nd set of x and y values.
m = (22600 - 15400) / (13 - 7) = 7200 / 6 = 1200 is the slope of the data points, which says that the population grew by 7200 in 6 years, 2007 to 2013.
For the y-intercept, b, just plug in your slope (m = 7200) and then your choice of data points (x1, y1) OR (x2, y2) into the f(t) = mt + b formula, where f(t) = y and t = x.
Then f(x1) = mx1 + b => 15400 = 7200*(7) = b => 15400 = 50400 + b
Solving for b... 15400 - 50400 = 50400 - 54000 + b => -35000 = 0 + b = b
Thus f(t) = mt + b is f(t) = 7200*t - 35000 upon substitution of m and b into the equation.
Part B: Use the model from Part B to approximate the population in 2020.
Using the model you found in part (a), f(t) = 7200*t - 35000, just know that t is the number of years after 2020...which is 2020 - 2000 = 20 years, so t = 20
Now f(20) = 7200*20 - 35000 = 144,000 - 35,000 = 109,000! A fast growing town!