The function y = 4(6)^t models the number of people who have watched a video after...
Check the final answer first, then review the worked steps.
Problem
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
4
Step-by-step solution
1. Identify the function: The given function is $y = 4(6)^t$, where $y$ represents the number of people who have watched a video after $t$ days.
2. Understand the y-intercept: The y-intercept is the point where the graph of the function crosses the y-axis. This occurs when the independent variable (in this case, $t$) is equal to 0.
3. Calculate the y-intercept: To find the y-intercept, substitute $t=0$ into the function:
$$y = 4(6)^0$$
4. Evaluate the exponent: Any non-zero number raised to the power of 0 is 1. So, $6^0 = 1$.
5. Solve for y: Substitute the value of $6^0$ back into the equation:
$$y = 4(1)$$
$$y = 4$$
6. Interpret the result: The y-intercept is 4. This means that initially, when $t=0$ days, 4 people had watched the video.