Exponential vs. Linear Question 4

\begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 \\ \hline \\ y & \frac{12}{5} & \frac{17}{5} & \frac{22}{5} & \frac{27}{5} & \frac{32}{5} \\ \\ \hline \end{array}

Which of the following equations related $y$ to $x$ for the values in the table above?

y=\dfrac{12}{2}\cdot \left(\dfrac{2}{5}\right)^x

y= \dfrac{7}{5}\cdot (5)^x

y=x+\dfrac{7}{5}

y=\dfrac{12}{5}x

Approach

We can test our models, but we should first figure out if the table represents a linear or an exponential model. From the table, choosing a few pairs:

\frac{32}{5}-\frac{27}{5}

= \frac{5}{5}

=1

\frac{17}{5}-\frac{12}{5}

=\frac{5}{5}

=1

This represents a rate of change of $1$ , or a slope of $1$ in a linear equation. Only one answer choice represents this.