The problem asks for the y-intercept of the exponential function $y = 0.5(6)^x$.

Solution:

The y-intercept occurs when $x = 0$. Substituting $x = 0$ into the equation:

$y = 0.5(6)^x$

$y = 0.5(6)^0$

Since $6^0 = 1$:

$y = 0.5 \times 1 = 0.5$

Final Answer:

The y-intercept is 0.5.

Would you like a step-by-step graphing explanation or have any questions?

Here are 5 related questions to expand your understanding:

1. What is the significance of the base $6$ in the function $y = 0.5(6)^x$?
2. How does the coefficient $0.5$ affect the graph of the exponential function?
3. What happens to the y-intercept if the coefficient changes to $1$?
4. How would the graph look if the base were less than $1$ (e.g., $y = 0.5(0.6)^x$)?
5. How do you find the y-intercept for more complex functions like $y = 0.5(6)^{x-2} + 1$?

Tip:

Remember, for any function, the y-intercept is found by substituting $x = 0$ into the equation.