Question

the scatter plot shows the population p of a town (in thousands) t years after 2000. which is the best linear equation to model the towns population from 2000 to 2010? p(t)=0.20t + 1.12 p(t)=1.12t + 0.02 p(t)=1.12t + 0.20 p(t)=0.02t + 1.12

Explanation:

Step1: Recall the slope - intercept form

The linear equation is of the form $P(t)=mt + b$, where $m$ is the slope and $b$ is the $y$-intercept (in this case, population when $t = 0$).

Step2: Estimate the $y$-intercept

When $t = 0$ (year 2000), from the scatter - plot, the population $P(0)$ is approximately $1.12$ thousand. So $b\approx1.12$.

Step3: Estimate the slope

The population increases from about $1.12$ thousand at $t = 0$ to about $1.2$ thousand at $t=4$. The slope $m=\frac{\Delta P}{\Delta t}=\frac{1.2 - 1.12}{4}=\frac{0.08}{4}=0.02$.

Answer:

$P(t)=0.02t + 1.12$