Question

practice and problem solve:
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?
using #4 and 5 from example 1:

• explain how the answers could be predicted using the graph.
• explain which question involved interpolation and which involved extrapolation. explain your answer.
• explain why using the model would give more accurate predictions.

summary/homework:

Explanation:

Step1: Find the value of \(x\) for 2040

The year 2040 is \(2040 - 1920=120\) years since 1920. So \(x = 120\).

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

Substitute \(x = 120\) into the equation: \(y=2.33\times120+92.05\).
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:

The projected U.S. population in 2040 is \(371.65\) million people.