Question

1. the graph shows the total distance, in feet, traveled by a person as a function of time, in seconds, find the average rate of change between 40 and 140 seconds.

Explanation:

Step1: Identify coordinates at t=40 and t=140

At \( t = 40 \) seconds, from the graph, the distance \( d(40) = 10 \) feet. At \( t = 140 \) seconds, the distance \( d(140) = 30 \) feet (assuming the top grid line is 30, as the graph shows progression; visually, at 140, it's 30 feet).

Step2: Apply average rate of change formula

The formula for average rate of change of a function \( d(t) \) between \( t = a \) and \( t = b \) is \( \frac{d(b)-d(a)}{b - a} \). Here, \( a = 40 \), \( b = 140 \), \( d(40)=10 \), \( d(140)=30 \). So, \( \frac{30 - 10}{140 - 40}=\frac{20}{100}=0.2 \).

Answer:

The average rate of change is \( 0.2 \) feet per second.