sat-dog

The correct answer is $257$. It’s given that a linear model estimates the population of a city from $1991$ to $2015$. Since the population can be estimated using a linear model, it follows that there is a constant rate of change for the model. It’s also given that the model estimates the population was $57$ thousand in $1991$, $224$ thousand in $2011$, and $x$ thousand in $2015$. The change in the population between $2011$ and $1991$ is $224-57$, or $167$, thousand. The change in the number of years between $2011$ and $1991$ is $2011-1991$, or $20$, years. Dividing $167$ by $20$ gives $167/20$, or $8.35$, thousand per year. Thus, the change in population per year from $1991$ to $2015$ estimated by the model is $8.35$ thousand. The change in the number of years between $2015$ and $2011$ is $2015-2011$, or $4$, years. Multiplying the change in population per year by the change in number of years yields the increase in population from $2011$ to $2015$ estimated by the model: $\left(8.35\right)\left(4\right)$, or $33.4$, thousand. Adding the change in population from $2011$ to $2015$ estimated by the model to the estimated population in $2011$ yields the estimated population in $2015$. Thus, the estimated population in $2015$ is $33.4+224$, or $257.4$, thousand. Therefore to the nearest whole number, the value of $x$ is $257$.