1. The problem asks to find the best linear equation to model the town's population $P$ (in thousands) as a function of time $t$ years after 2000, from 2000 to 2010. 2. A linear model has the form $$P(t) = mt + b$$ where $m$ is the slope (rate of change of population per year) and $b$ is the initial population at $t=0$ (year 2000). 3. From the scatter plot description, the population increases roughly linearly from left to right, so the slope $m$ should be positive but relatively small since population growth is usually gradual. 4. Let's analyze each option: - $P(t) = 0.02t + 1.12$: slope $m=0.02$, intercept $b=1.12$ - $P(t) = 1.12t + 0.20$: slope $m=1.12$, intercept $b=0.20$ - $P(t) = 1.12t + 0.02$: slope $m=1.12$, intercept $b=0.02$ - $P(t) = 0.20t + 1.12$: slope $m=0.20$, intercept $b=1.12$ 5. Since the population is in thousands, an intercept around 1.12 means 1120 people at year 2000, which is reasonable. 6. The slope $m$ represents the increase in population per year in thousands. A slope of 1.12 means an increase of 1120 people per year, which is quite large for a small town. 7. A slope of 0.02 means an increase of 20 people per year, which is very small. 8. A slope of 0.20 means an increase of 200 people per year, which is reasonable. 9. Therefore, the best linear model is $$P(t) = 0.20t + 1.12$$ which balances a reasonable initial population and a plausible growth rate. Final answer: $$\boxed{P(t) = 0.20t + 1.12}$$