The population of Arizona was 5.1 million in 2000 and 7.7 million in 2008. If the population grew linearly which one of the following models the population as a function of time (in years since 2000)?

Question

Quizplus · Accepted Answer

We need to find the equation of the line that passes through the points $(0, 5.1)$ and $(8, 7.7)$, where the $x$-axis represents the years since 2000 and the $y$-axis represents the population in millions. Using the slope-intercept form of a linear equation, we have: $$y = mx + b,$$ where $m$ is the slope and $b$ is the $y$-intercept.

The slope $m$ is given by: $$m = \frac{	ext{change in } y}{	ext{change in } x} = \frac{7.7-5.1}{8-0} = \frac{2.6}{8} = 0.325.$$

To find the $y$-intercept $b$, we can plug in the values of $x$ and $y$ from one of the points: $$5.1 = 0.325(0) + b \quad \Rightarrow \quad b = 5.1.$$

Thus, the equation of the line is: $$y = 0.325 x + 5.1.$$

This means that the population $P$ (in millions) as a function of the years $t$ since 2000 can be modeled by the equation: $$P(t) = 0.325 t + 5.1.$$

Therefore, the answer is choice (B).

The Population of Arizona Was 5