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: \([0, 2,704]\).