Answer
A) Linear
B) $$
\begin{aligned}
i(x)& =18-4x \\
\end{aligned}
$$
Work Step by Step
Given
$$
\begin{array}{c|c}
\hline x & i(x) \\
\hline 0 & 18 \\
1 & 14 \\
2 & 10 \\
3 & 6 \\
4 & 2 \\
\hline
\end{array}
$$
A) We know that a function is linear if the differences of successive values of the function is a constant. A function is exponential if the ratios of successive values of the function is a constant.
$$
\begin{aligned}
&i(1)-i(0)=14-18=-4\\
&i(2)-i(1)=10-14=-4 .
\end{aligned}
$$
Thus, the function is linear.
B) We know that
$$
i(x)=mx+b
$$
The table shows that $x=0$ and $i(0) = 18= b$.
Thus,
$$
\begin{aligned}
i(1) & =b+m \cdot 1 \\
14 & =18+m \\
m & =-4 .
\end{aligned}
$$
Hence:
$$
\begin{aligned}
i(x)& =18-4x \\
\end{aligned}
$$
