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.(1 point)

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 \( t = 0 \).

Let's calculate \( y \) when \( t = 0 \):

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

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

\[
y = 4(1) = 4
\]

So, the y-intercept is \( 4 \). This means that initially, 4 people watched the video.

To visualize this, you would graph the function \( y = 4(6)^t \):

1. Start at the point \( (0, 4) \) on the y-axis.
2. As \( t \) increases, \( y \) will increase rapidly because of the exponential growth factor of 6.

The graph would show a steep rise as \( t \) increases, demonstrating the rapid increase in viewership after the initial 4 people watched the video.

In summary, **4 people initially watched the video**.