Answer:
[tex]y=8\cdot \left(\dfrac{1}{2}\right)^x.[/tex]
Step-by-step explanation:
If the graph of exponential function passes through the points (0,8) and (6,0.125), then the coordinates of these points sutisfy the equation [tex]y=a\cdot b^x:\\[/tex]
[tex]8=a\cdot b^0\Rightarrow a=8,\\ \\0.125=8\cdot b^6\Rightarrow \dfrac{1}{8}=8\cdot b^6,\\ \\b^6=\dfrac{1}{64},\\ \\b^6=\dfrac{1}{2^6}\Rightarrow b=\dfrac{1}{2}.[/tex]
Thus, the equation of exponential function is
[tex]y=8\cdot \left(\dfrac{1}{2}\right)^x.[/tex]
