B.
Step-by-step explanation:
To find the right exponential function, we can just take x-values an replace them into the given functions. The one that give the correct y-values will be the answer.
For
, let's see which function gives ![y=-\frac{1}{8}](/tpl/images/0372/7512/0e8d1.png)
![y=8(4)^{x-1} \\y=8(4)^{-2-1}\\ y=8(4)^{-3}\\ y=\frac{8}{4^{3} }=\frac{1}{8}](/tpl/images/0372/7512/b320c.png)
You can observe that function A is not the correct one, because it gives a positive result. However, function B can actually be the answer, because it woud give the same y-value than A but negative, as we need. Let's see
![y=-8(4)^{x-1}\\ y=-8(4)^{-2-1}\\ y=-8(4)^{-3}\\ y=-\frac{8}{4^{3} }=-\frac{1}{8}](/tpl/images/0372/7512/95c63.png)
Let's evalute for ![x=0](/tpl/images/0372/7512/37eb6.png)
![y=-8(4)^{0-1}=-8(4)^{-1}= -\frac{8}{4}=-2](/tpl/images/0372/7512/af272.png)
Which is right.
Therefore, the right answer is B.