Question

1. a climber is on a hike. after 2 hours he is at an altitude of 400 feet. after 6 hours, he is at an altitude of 700 feet. what is the average rate of change? a) 300 b) 200 c) 150 d) 75

Explanation:

Step1: Recall the formula for average rate of change

The formula for average rate of change is $\frac{\text{Change in altitude}}{\text{Change in time}}$.

Step2: Calculate the change in altitude

The initial altitude is 400 feet (at 2 hours) and the final altitude is 700 feet (at 6 hours). So the change in altitude is $700 - 400 = 300$ feet.

Step3: Calculate the change in time

The initial time is 2 hours and the final time is 6 hours. So the change in time is $6 - 2 = 4$ hours.

Step4: Calculate the average rate of change

Using the formula, we have $\frac{300}{4} = 75$ feet per hour.

Answer:

d) 75