The U.S. Bureau of the Census predicted that the population of Florida would be about 17.4 million in 2010 and then would increase by about 0.22 million per year until 2015. Which of the following linear models predicts the population, y, of Florida (in millions) in terms of x, the number of years since 2010.

Question

y = mx + b
A. y = 17.4x + 0.22
B. y = -0.22x + 17.4
C. y = 0.22x + 17.4
D. y = -17.4x + 0.22

Answer 1

To create a linear model that predicts the population \( y \) (in millions) of Florida based on the number of years \( x \) since 2010, we can use the information given:

1. The population in 2010 (when \( x = 0 \)) is 17.4 million.
2. The population increases by 0.22 million per year.

The linear equation is typically represented as:

\[ y = mx + b \]

where:

• \( m \) is the slope (the rate of change, which is the increase in population per year),
• \( b \) is the y-intercept (the population at the starting year, 2010 in this case).

From the information provided:

• The initial population in 2010 is 17.4 million, which means \( b = 17.4 \).
• The population increases by 0.22 million per year, which means \( m = 0.22 \).

So the equation becomes:

\[ y = 0.22x + 17.4 \]

This matches option C. Therefore, the correct answer is:

C. \( y = 0.22x + 17.4 \)