Question

The function f(t) = 3(2)^t
models the number of people who visited a pumpkin patch since it opened after t hours.
Part B: The y-intercept is
(write your answer as an ordered pair).

Part C: The domain of function given the context of this situation is t >

Answer 1

Part B: To find the y-intercept of the function \( f(t) = 3(2)^t \), we need to evaluate the function at \( t = 0 \).

\[
f(0) = 3(2)^0 = 3(1) = 3
\]

The y-intercept is the point where the graph of the function intersects the y-axis, which corresponds to the point when \( t = 0 \). Therefore, the y-intercept is:

\[
(0, 3)
\]

Part C: Given the context of the situation, \( t \) represents the number of hours since the pumpkin patch opened. This implies that time cannot be negative. Therefore, the domain of the function is:

\[
t \geq 0
\]

In conclusion:
- Part B: The y-intercept is \( (0, 3) \).
- Part C: The domain of the function given the context is \( t \geq 0 \).