Question

You are climbing a 500 -foot cliff. By 1: 00 P.M. you have climbed 125 feet up the cliff. By 4: 00 P.M. you have reached a height of 290 feet. What is your rate of change in height?

Short answer

The rate of change in height is 55 feet/hour.

Step-by-step solution

Identify the heights and corresponding times

The climber starts at 125 feet at 1:00 p.m. and by 4:00 p.m., the climber has reached 290 feet. This gives two points (1,125) and (4,290) where the first component of the point represents the time in PM and the second component represents corresponding height in feet.

Determine the change in height and time

The change in height delta(h) is the difference between the final height and the initial height. So, delta(h) = 290 - 125 = 165 feet. The change in time delta(t) is the difference between the final time and the initial time. So, delta(t) = 4 - 1 = 3 hours.

Compute the rate of change

The rate of change is given by the formula: rate of change = delta(h) / delta(t) = 165 / 3 = 55 feet/hour.