inum is sitting on the beach, watching the tide go in and out.\ninums distance from the shoreline (in…

inum is sitting on the beach, watching the tide go in and out.\ninums distance from the shoreline (in meters) as a function of time (in hours) is graphed.\nwhat is the approximate average rate at which inums distance from the shoreline increases, between the $9^{th}$ and the $13^{th}$ hour marks?\nchoose 1 answer:\n0.75 meters per hour\n1 meter per hour\n1.25 meters per hour\n1.5 meters per hour

inum is sitting on the beach, watching the tide go in and out.\ninums distance from the shoreline (in meters) as a function of time (in hours) is graphed.\nwhat is the approximate average rate at which inums distance from the shoreline increases, between the $9^{th}$ and the $13^{th}$ hour marks?\nchoose 1 answer:\n0.75 meters per hour\n1 meter per hour\n1.25 meters per hour\n1.5 meters per hour

Answer

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