Graph the exponential function \( y=0.5(6)^{x} \). Identify the \( y \)-intercept. (1 point) 1 0.5 0 -4

To graph the function \( y = 0.5(6)^{x} \), start by plotting the y-intercept, which occurs when \( x = 0 \). Plugging in \( x = 0 \) gives you \( y = 0.5(6^0) = 0.5(1) = 0.5 \). This means the y-intercept is 0.5, which is point (0, 0.5) on the graph. As \( x \) increases, the function rapidly rises due to the exponential growth from the base of 6, creating a steep curve upward. Exponential functions have a fascinating behavior that makes them important in real-world applications. For example, they model populations, radioactive decay, and financial growth (like compound interest). In each case, small changes in the growth rate can lead to dramatic differences over time—a phenomenon that's both exhilarating and cautionary in fields from ecology to finance!