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 the average rate of change of a function $y = f(x)$ over the interval $[x_1,x_2]$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here, $x$ represents time (in hours) and $y$ represents altitude (in feet). $x_1 = 2$, $y_1=400$, $x_2 = 6$, $y_2 = 700$.

Step2: Substitute values into the formula

$\frac{y_2 - y_1}{x_2 - x_1}=\frac{700 - 400}{6 - 2}$

Step3: Calculate the result

$\frac{700 - 400}{6 - 2}=\frac{300}{4}=75$

Answer:

75 feet per hour