Final answer:
To estimate the US population for any year after 2010 based on the given data, we calculate the slope of the population increase between 2010 and 2020 and use point-slope form to derive the equation: y = 21834563.6x + 308745538.
Step-by-step explanation:
To write an equation in point-slope form that represents the US population at any time given two points of data, we first need to find the slope of the line connecting these points.
We are given the US population as 308,745,538 in 2010 and 330,580,174 in 2020. Let x represent the number of years after 2010. Therefore, we have two points: (0, 308745538) and (10, 330580174).
To find the slope (m), which represents the annual change in population, we use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are our two points. Thus:
m = (330580174 - 308745538) / (10 - 0) = 218345636 / 10 = 21834563.6
The point-slope form of the equation is given by (y - y1) = m(x - x1). Substituting the slope we found and the year 2010 point, we get:
(y - 308745538) = 21834563.6(x - 0)
Simplifying, we have the final equation:
y = 21834563.6x + 308745538
This equation can estimate the US population in any year x after 2010, assuming the same rate of growth continues.