The relationship between the sound level in a room and the rate at
which people wake up can be modeled by a linear function as shown.
Which of these best describes the
rate of change of the frequency of
people waking up with respect to
the sound level?
Frequency of People Waking Up
vs. Sound Level
100
8% per 9 decibels
90
80
B
3% per 4 decibels
70
60
9% per 8 decibels
Frequency of People Waking Up (%)
50
40
4% per 3 decibels
30
20
10
0 145
55 65 75 85 95 105 115
Sound Level (decibels)

Linear function is the function in which the highest power of the unknown variable is one. Linear functions used to model the real life problem in the mathematical expressions.

The linear function with dependent variable y and independent variable x can be written as,

[tex]y=mx +c[/tex]

Here, (m) is the slope of the function and (c) is the y intercept.

The slope can be found out as,

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The sound level is plotted on x-axis and frequency of people walking up (%) is plotted on y-axis. The slope of the line given the rate of change of y values with respect to x value.

In the graph given, the frequency of people walking up is 10 at 55 decibels and 55 at 95 decibels. The point, we get for this line are (55, 10) and (95, 55). Therefore the slope or the change of rate is,

[tex]\dfrac{dy}{dx}=\dfrac{55-10}{95-55}\\\dfrac{dy}{dx}=\dfrac{45}{40}\\\dfrac{dy}{dx}=\dfrac{9}{8}[/tex]

Hence, the change of the frequency of people waking up with respect to the sound level, 9% per 8 decibels.

Learn more about the linear function here;

https://brainly.com/question/15602982