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.

Question

The y-intercept is at the point (0, ___).

Answer 1

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

So, we calculate:

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

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

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

Therefore, the y-intercept is at the point \( (0, 30) \).

So, the answer is:

The y-intercept is at the point \( (0, 30) \).