Because $x$ increases by $2$ in each row, the exponent $x/2$ increases by $1$. In a shifted exponential model, consecutive changes are multiplied by the base $b$.

After finding $b$, use two data points to write two equations involving $a$ and $c$. Then evaluate the resulting model at $x=7$.

Algebra is faster here because the doubling pattern in the consecutive changes identifies the base. Desmos can verify the resulting model.

Enter the table values in a Desmos table. Then graph $y=6(2)^{x/2}-1$. The curve passes through all four data points.

Enter $6(2)^{7/2}-1$ on a new expression line. Desmos displays a decimal approximation for the predicted value; compare that approximation with the answer choices.

For consecutive rows, the changes in $y$ are $6$, $12$, and $24$. These changes double each time $x$ increases by $2$.

For a model of the form $y=a(b)^{x/2}+c$, the changes over equal increases in $x$ are multiplied by $b$. Therefore, $b=2$.

Using the first two data points gives

Subtracting the first equation from the second gives $a=6$. Then $c=5-6=-1$.

So the model is $y=6(2)^{x/2}-1$.

Substitute $x=7$:

This is choice B.