Question

1. consider the two graphs showing population growth of the world and the united states. notice that the two graphs appear at first glance to have similar slopes.

a. estimate the average rate of change from 1960 to 2000 for the world population. write a sentence interpreting the meaning of this answer.
b. estimate the average rate of change from 1960 to 2000 for the us population. write a sentence interpreting the meaning of this answer.
c. would you consider the rates of changes for the two graphs to be similar?

Explanation:

Step1: Find the average rate of change formula

The average rate of change formula is $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$, where $y$ represents population (in millions) and $x$ represents the year.

Step2: Estimate values for world population

For the world population in 1960 ($x_1 = 1960$, $y_1\approx2800$) and 2000 ($x_2 = 2000$, $y_2\approx5200$).
$\frac{y_2 - y_1}{x_2 - x_1}=\frac{5200 - 2800}{2000 - 1960}=\frac{2400}{40}=60$
Interpretation: The world population increased at an average rate of 60 million people per year from 1960 to 2000.

Step3: Estimate values for US population

For the U.S. population in 1960 ($x_1 = 1960$, $y_1\approx180$) and 2000 ($x_2 = 2000$, $y_2\approx280$).
$\frac{y_2 - y_1}{x_2 - x_1}=\frac{280 - 180}{2000 - 1960}=\frac{100}{40}=2.5$
Interpretation: The U.S. population increased at an average rate of 2.5 million people per year from 1960 to 2000.

Step4: Compare the rates

The rate of change for the world population ($60$ million per year) and the U.S. population ($2.5$ million per year) are not similar.

Answer:

a. The average rate of change for the world population is $60$ million people per year. The world population increased at an average rate of 60 million people per year from 1960 to 2000.
b. The average rate of change for the U.S. population is $2.5$ million people per year. The U.S. population increased at an average rate of 2.5 million people per year from 1960 to 2000.
c. No, the rates of changes for the two graphs are not similar.