The function f(t) = 3(2)^t

Question

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 \( t \geq 0 \).