The table shows how an elevator 500 feet above the ground is descending at a steady rate.

A two column table with 5 rows. The first column, time in seconds (t), has the entries, 0, 5, 10, 15. The second column, Height in feet h(t), has the entries, 500, 475, 450, 425.
Which equation represents the height, h(t), of the elevator in feet, as a function of t, the number of seconds during which it has been descending?

h(t) = 5t + 500
h(t) = 5t – 500
h(t) = –5t + 500
h(t) = –5t – 500

1 answer

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: \[ \boxed{h(t) = -5t + 500} \]