Using the discussed properties of exponential decay graphs, find the y-intercept of the function: y = 30(0.85)x, that models an exponential sequence.

1 answer

To find the y-intercept of the function \( y = 30(0.85)^x \), we evaluate the function at \( x = 0 \).

The y-intercept occurs where the graph intersects the y-axis, which corresponds to the value of \( y \) when \( x = 0 \):

\[ y = 30(0.85)^0 \]

Since any number raised to the power of 0 is 1, we have:

\[ y = 30 \cdot 1 = 30 \]

Thus, the y-intercept of the function \( y = 30(0.85)^x \) is:

\[ \boxed{30} \]