Question

inum is sitting on the beach, watching the tide go in and out.
inums distance from the shoreline (in meters) as a function of time (in hours) is graphed.
what is the approximate average rate at which inums distance from the shoreline increases, between the $9^{th}$ and the $13^{th}$ hour marks?
choose 1 answer:
0.75 meters per hour
1 meter per hour
1.25 meters per hour
1.5 meters per hour

Explanation:

Step1: Recall the average rate of change formula

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, \(a = 9\), \(b=13\), \(x\) represents time (in hours) and \(y\) represents the distance from the shoreline (in meters).

Step2: Estimate the function values from the graph

From the graph, when \(x = 9\), \(y=f(9)\approx6\) meters and when \(x = 13\), \(y = f(13)\approx9\) meters.

Step3: Calculate the average rate of change

Substitute into the formula: \(\frac{f(13)-f(9)}{13 - 9}=\frac{9 - 6}{13-9}=\frac{3}{4}=0.75\)

Answer:

A. \(0.75\) meters per hour