The document discusses using an equation to model population growth in the United States between 2010 and 2050. It states that the 2010 population was 300 million and is expected to increase by 2.5 million per year. An equation is provided to calculate the population P in any given year x: P = 2.5x + 300. Using this equation, the document determines that the predicted population in 2050 is 400 million.

1. USING EQUATIONS OF
LINES
AN EXAMPLE WITH POPULATION

2. The population of the United States
was about 300 million in the year
2010.
Between 2010 and 2050, the
population is expected to increase
by about 2.5 million per year.

3. a. Write an equation to find the
population P in any year x between
2010 and 2050.
b. Find the population in 2050.

4. THE SOLUTION

5. a. Write an equation to find the population P
in any year x between 2010 and 2050.
The rate of change is 2.5 million per year. The rate
of change is positive because this is an increase. In
the first year, 2010, the population is 2.5. Let P
equal the population in the United States. Let x
equal the number of years after 2010.
An equation is P = 2.5x + 300

6. b. Find the population in 2050.
If the year is 2050, that is 40 years after the year 2010.
So let x = 40.
P = 2.5x + 300
P = 2.5(40) + 300
P = 100 + 300
P = 400
The population is 2050 will be 400 million.