Question

The functionf(t) = 3(2)t
models the number of people who visited a pumpkin patch since it opened after t hours.



(1 point)
Part A: Fill out the table below.

t f(t)
0
2
5
7
10
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 >

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Answer 1

Let's start by calculating \( f(t) = 3(2)^t \) for the specified values of \( t \).

### Part A: Fill in the table

1. **For \( t = 0 \)**:
\[
f(0) = 3(2)^0 = 3(1) = 3
\]

2. **For \( t = 2 \)**:
\[
f(2) = 3(2)^2 = 3(4) = 12
\]

3. **For \( t = 5 \)**:
\[
f(5) = 3(2)^5 = 3(32) = 96
\]

4. **For \( t = 7 \)**:
\[
f(7) = 3(2)^7 = 3(128) = 384
\]

5. **For \( t = 10 \)**:
\[
f(10) = 3(2)^{10} = 3(1024) = 3072
\]

### Completed Table:
\[
\begin{array}{|c|c|}
\hline
t & f(t) \\
\hline
0 & 3 \\
2 & 12 \\
5 & 96 \\
7 & 384 \\
10 & 3072 \\
\hline
\end{array}
\]

### Part B: The y-intercept
The y-intercept occurs when \( t = 0 \). Thus, the ordered pair for the y-intercept is:
\[
(0, 3)
\]

### Part C: The domain of the function
Given the context of the situation (people visiting a pumpkin patch), the time \( t \) must be greater than or equal to 0. Therefore, the domain is:
\[
t \geq 0
\]

Putting it together, the answers are:
1. Table filled out as shown.
2. Y-intercept: \( (0, 3) \)
3. Domain: \( t \geq 0 \) (or in a strict inequality context, \( t > -1 \)).