Question

The function y=4(6)^t
models the number of people who have watched a video after t
days. Graph the function to determine how many people initially watched the video by finding the y
-intercept.

Answer 1

To find the initial number of people who watched the video, we need to determine the y-intercept of the function \( y = 4(6)^t \).

The y-intercept occurs when \( t = 0 \). So, let's substitute \( t = 0 \) into the function:

\[
y = 4(6)^0
\]

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

\[
y = 4 \times 1 = 4
\]

Therefore, the y-intercept is \( 4 \). This means that initially, 4 people watched the video when \( t = 0 \).

If you were to graph the function \( y = 4(6)^t \):

1. At \( t = 0 \), the point would be (0, 4).
2. As \( t \) increases, the number of viewers would grow exponentially due to the base of 6.

In summary, the initial number of people who watched the video is **4**.