Answer:
![D.\ (3,(1)/(8))](https://img.qammunity.org/2022/formulas/mathematics/high-school/8ivwwnpz0uyd8v64rou7x5hs480iu7zzsr.png)
Explanation:
Given
![y = ((1)/(2))^x](https://img.qammunity.org/2022/formulas/mathematics/high-school/6q7hnncu2a9zxswjci3g1i7vl2aokaqwji.png)
Required
Points that lies on the above graph
From the given options, only option D lies on the point and the proof is as follows:
![D.\ (3,(1)/(8))](https://img.qammunity.org/2022/formulas/mathematics/high-school/8ivwwnpz0uyd8v64rou7x5hs480iu7zzsr.png)
This means that:
![x = 3;\ y = (1)/(8)](https://img.qammunity.org/2022/formulas/mathematics/high-school/72kujh0l5cnxx66xmi1wttqtwcjnmgah83.png)
Substitute
in
![y = ((1)/(2))^x](https://img.qammunity.org/2022/formulas/mathematics/high-school/6q7hnncu2a9zxswjci3g1i7vl2aokaqwji.png)
![(1)/(8) = ((1)/(2))^3](https://img.qammunity.org/2022/formulas/mathematics/high-school/x71orq71hle6a1rgaz99l1sq6jr69fn0ej.png)
![(1)/(8) = (1^3)/(2^3)](https://img.qammunity.org/2022/formulas/mathematics/high-school/tl368dor3jxngop6fo4kt7x1pouss9m83g.png)
![(1)/(8) = (1)/(8)](https://img.qammunity.org/2022/formulas/mathematics/high-school/4kgenzo299bzjul0qzsgkx6h68arrn8txx.png)
See that the values at the right and left hand side of the equation are the same.
This means that,
lies on
![y = ((1)/(2))^x](https://img.qammunity.org/2022/formulas/mathematics/high-school/6q7hnncu2a9zxswjci3g1i7vl2aokaqwji.png)