Question

directions - find the average rate of change for the word problem. also, label correct units. 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 between hour 2 and hour 7?

Explanation:

Step1: Identify the formula for average rate of change

The formula for average rate of change between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x\) represents time (in hours) and \(y\) represents altitude (in feet). So, \(x_1 = 2\), \(y_1 = 400\), \(x_2 = 6\), \(y_2 = 700\).

Step2: Substitute the values into the formula

Substitute the values into \(\frac{y_2 - y_1}{x_2 - x_1}\): \(\frac{700 - 400}{6 - 2}\)

Step3: Calculate the numerator and the denominator

First, calculate the numerator: \(700 - 400 = 300\). Then, calculate the denominator: \(6 - 2 = 4\). So now we have \(\frac{300}{4}\)

Step4: Simplify the fraction

Simplify \(\frac{300}{4}\) to get \(75\). The units for the average rate of change will be feet per hour (since we are finding the change in altitude over the change in time).

Answer:

The average rate of change is \(75\) feet per hour.