Question

A skydiver jumps from an airplane at a height of 2,704 feet. The function h = −16t2+2,704
models the height of the skydiver, h, in feet, with respect to time, t, in seconds. What is the reasonable domain and range of the polynomial function?(1 point)
Responses

Domain: [0,13][0,13];

Range: [0,∞)

Domain: [0,13][0,13]; Range: [0,∞)

Domain: (−∞,∞)(−∞,∞);

Range: (−∞,∞)

Domain: (−∞,∞)(−∞,∞); Range: (−∞,∞)

Domain: [0,13][0,13];

Range: [0,2,704]

Domain: [0,13][0,13]; Range: [0,2,704]

Domain: [0,∞)[0,∞);

Range: [0,2,704]

Answer 1

To understand the reasonable domain and range of the function \( h = -16t^2 + 2,704 \) for the skydiver, we can analyze the context of the situation.

### Domain:
- The function models the height of the skydiver as a function of time \( t \).
- The skydiver jumps from a height of 2,704 feet, which implies the jump starts at \( t = 0 \).
- The skydiver reaches ground level when \( h = 0 \). We can calculate the time when this happens by setting the height function to zero:

\[
0 = -16t^2 + 2,704
\]
\[
16t^2 = 2,704
\]
\[
t^2 = 169
\]
\[
t = 13 \quad (\text{since time cannot be negative})
\]

Thus, the time \( t \) can only realistically take values from 0 to 13 seconds. Therefore, the **domain** is:
\[
[0, 13]
\]

### Range:
- The height \( h \) starts at 2,704 feet (when \( t = 0 \)) and decreases to the ground level (0 feet at \( t = 13 \)).
- Therefore, the height \( h \) can take all values from 0 to the maximum height of 2,704 feet.

Thus, the **range** is:
\[
[0, 2,704]
\]

### Conclusion:
Putting it all together, the reasonable domain and range of the function are:
- **Domain**: \([0, 13]\)
- **Range**: \([0, 2,704]\)

**Final Answer:**
**Domain: \([0, 13]\); Range: \([0, 2,704]\)**.