To find the equation representing the height \( h(t) \) of the elevator as a function of time \( t \), we can analyze the data given in the table.
The elevator starts at 500 feet at time \( t = 0 \) seconds and descends to 475 feet at \( t = 5 \) seconds, then to 450 feet at \( t = 10 \) seconds, and down to 425 feet at \( t = 15 \) seconds.
From the data:
- Every 5 seconds, the elevator descends by 25 feet (from 500 to 475 feet, from 475 to 450 feet, and from 450 to 425 feet).
- This gives us a rate of descent of \( \frac{25 \text{ feet}}{5 \text{ seconds}} = 5 \text{ feet per second} \).
Since the elevator is descending, the height decreases as time increases, which indicates a negative slope in the equation.
The general form of the equation is: \[ h(t) = mt + b \] where \( m \) is the slope and \( b \) is the y-intercept (the initial height).
From our information:
- The slope \( m = -5 \) (indicating a descent of 5 feet per second),
- The y-intercept \( b = 500 \) (the initial height at \( t = 0 \)).
Therefore, the equation is: \[ h(t) = -5t + 500 \]
So the correct answer is: \[ \boxed{h(t) = -5t + 500} \]
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