The function y = 3(2)t

Question

models the number of people who visit a haunted house since it opened after t hours.

Graph the function using desmos to determine how many people initially visited the haunted house when it opened by finding the y-intercept.

Answer 1

To determine how many people initially visited the haunted house, we need to find the y-intercept of the function \( y = 3(2)^t \).

The y-intercept occurs when \( t = 0 \). We can substitute \( t = 0 \) into the function:

\[ y = 3(2)^0 \]

Since \( (2)^0 = 1 \), this simplifies to:

\[ y = 3 \cdot 1 = 3 \]

Therefore, the y-intercept is \( y = 3 \). This means that initially, when the haunted house opened, 3 people visited.

To visualize this using Desmos:

1. Go to the Desmos graphing calculator.
2. Enter the function \( y = 3(2)^t \) into the input field.
3. Observe the graph, and locate the point where it intersects the y-axis (the y-intercept), which will confirm that the initial number of visitors is 3.

If you follow these steps, you will see that the y-intercept on the graph is indeed at \( (0, 3) \).