To find the y-intercept of the function \( y = \frac{1}{5}(2)^x \), we can substitute \( x = 0 \) into the equation.
Calculating this:
\[ y = \frac{1}{5}(2)^0 \] Since \( (2)^0 = 1 \):
\[ y = \frac{1}{5}(1) = \frac{1}{5} \]
The y-intercept is the point where the graph intersects the y-axis, which occurs at \( x = 0 \). Therefore, when \( x = 0 \), \( y = \frac{1}{5} \).
Thus, the y-intercept is:
\[ (0, \frac{1}{5}) \]
To summarize, the y-intercept for the function \( y = \frac{1}{5}(2)^x \) is \( (0, \frac{1}{5}) \).