Question

darren collects data on the u.s. population from 1920 to 2020. he graphs the population and the number of years since 1920 in the scatter plot shown.
he determines the equation for the line of best fit to be ( y = 2.33x + 92.05 ) where ( y ) represents the population, in millions of people, and ( x ) represents the number of years since 1920.
based on darrens model, what is the projected u.s. population, in millions of people, for 2040?

Explanation:

Step1: Calculate the number of years from 1920 to 2040

To find \(x\), we subtract 1920 from 2040.
\(x = 2040 - 1920=120\)

Step2: Substitute \(x = 120\) into the equation \(y = 2.33x+92.05\)

We use the linear equation \(y = 2.33x + 92.05\). Substitute \(x = 120\) into it.
\(y=2.33\times120 + 92.05\)
First, calculate \(2.33\times120\):
\(2.33\times120=(2 + 0.33)\times120=2\times120+0.33\times120 = 240+39.6 = 279.6\)
Then add \(92.05\) to the result:
\(y=279.6+92.05 = 371.65\)

Answer:

\(371.65\)