During the discussed properties of exponential decay graphs find the y-intercept of the function y = 30(0.85)^x that models an exponential sequence

Answer 1

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

The y-intercept occurs 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 \( 30 \).

In coordinate form, the y-intercept is at the point \( (0, 30) \).