Question

1. the number of visitors to the jacksonville zoos koana ice stand over a 5 - hour period is represented by the graph shown. determine the average rate of change over the interval (1leq xleq3)

Explanation:

Step1: Identify points at x=1, x=3

From the graph, at \( x = 1 \), let's assume the number of visitors (y - value) is 20 (since the point at x=1 is on the 20 - line). At \( x = 3 \), assume the y - value is 60 (since the point at x = 3 is on the 60 - line).

Step2: Apply average rate of change formula

The formula for the average rate of change of a function \( y = f(x) \) over the interval \( [a,b] \) is \( \frac{f(b)-f(a)}{b - a} \). Here, \( a = 1 \), \( b = 3 \), \( f(1)=20 \), \( f(3)=60 \).
So, average rate of change \(=\frac{60 - 20}{3 - 1}=\frac{40}{2}=20 \).

Answer:

The average rate of change over the interval \(1\leq x\leq3\) is \(20\) visitors per hour.