Question

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?
$h(t) = 5t + 500$
$h(t) = 5t - 500$
$h(t) = -5t + 500$
$h(t) = -5t - 500$

Explanation:

Step1: Identify initial height

The elevator starts at 500 feet (the constant term in the linear function, as height when \(t=0\)).

Step2: Identify rate of change

The elevator is descending, so the slope (rate of height change) is negative. A descent rate of 5 ft/s means slope = -5.

Step3: Form linear function

Linear height function: \(h(t) = \text{slope} \times t + \text{initial height}\)
Expression: \(h(t) = -5t + 500\)

Answer:

h(t) = -5t + 500