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An expression estimating the average rent of a one-bedroom apartment in Portland, Oregon, from January, 2011 to October, 2016, is given by $10.173x+974.78\text{,}$ where $x$ is the number of months since January, 2011.

According to this model, what was the average rent of a one-bedroom apartment in Portland in January, 2011?

According to this model, what was the average rent of a one-bedroom apartment in Portland in January, 2016?

Solution

This model uses $x$ as the number of months after January, 2011. So in January, 2011, $x$ is $0\text{:}$
$\begin{aligned} 10.173x+974.48 \amp=10.173(\substitute{0})+974.48\\ \amp \approx 974.48 \end{aligned}$
According to this model, the average monthly rent for a one-bedroom apartment in Portland, Oregon, in January, 2011, was $\$974.78\text{.}$

The date we are given is January, 2016, which is $5$ years after January, 2011. Recall that $x$ is the number of months since January, 2011. So we need to use $x=60\text{:}$
$\begin{aligned} 10.173x+974.48 \amp=10.173(\substitute{60})+974.48\\ \amp \approx 1584.86 \end{aligned}$
According to this model, the average monthly rent for a one-bedroom apartment in Portland, Oregon, was $\$1584.86$ in January 2016.