The graph represents a decreasing function. We can see that because when x increases, the corresponding y decreases.
Also, the options show exponential functions, i.e., with the variable x in the exponent.
So, in order to solve this problem, we need to analyze the options to find which of them can describe the graph.
Notice that:
[tex]\begin{gathered} \text{for a > 1, }a^x\text{ increases when x increases} \\ \\ \text{for 0 < a < 1, }a^x\text{ decreases when x increases} \end{gathered}[/tex]
Thus, for an exponential function to be an increasing function, a positive base, which has x as an exponent, needs to be less than 1.
And the only possible equation that satisfies that requirement is the one with base 1/2:
[tex]y=\mleft(\frac{1}{2}\mright)^x+6[/tex]
Notice that this equation indeed describes the graph, since for x = 0:
[tex]y=\mleft(\frac{1}{2}\mright)^0+6=1+6=7[/tex]
Therefore, option B is correct.
