Question

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.

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

What is the meaning of the slope in context?

Answer 1

To create a linear model predicting the population \( y \) of Florida (in millions) in terms of \( x \), the number of years since 2010, we start with the information provided.

The population in 2010 is given as approximately 17.4 million. The population increases by about 0.22 million each year.

We can express this situation with the equation of a line \( y = mx + b \), where:
- \( b \) is the population at \( x = 0 \) (which corresponds to the year 2010).
- \( m \) is the slope, representing the rate of change of population per year.

From the information:
- The initial population \( b = 17.4 \).
- The rate of change (slope) \( m = 0.22 \) (indicating that the population is increasing).

Thus, the model predicting the population can be written as:
\[ y = 0.22x + 17.4 \]

This matches option **C**: \( y = 0.22x + 17.4 \).

### Meaning of the Slope in Context
The slope \( m = 0.22 \) represents the annual increase in the population of Florida, measured in millions. In this context, it means that for each year after 2010 (each unit increase in \( x \)), the population is expected to increase by approximately 0.22 million (or 220,000 people).