Question

a study is being conducted to assess the amount of sleep emergency responders are getting when working a 24 hour shift. the scatter plot below shows the data collected from one of the fire stations surveyed. the plot compares the number of emergency calls the station received from 7pm to 7am and how many ours of sleep the firefighters had during that time period
what kind of function best describes the relationship between number of calls and hours of sleep?
a decreasing quadratic
b increasing quadratic
c decreasing linear
d increasing linear

Explanation:

Step1: Analyze the trend of the scatter - plot

In a scatter - plot, if the data points follow a straight - line pattern, it is a linear relationship. If they follow a parabolic pattern, it is a quadratic relationship.

Step2: Determine the direction of the relationship

As the number of calls (x - axis) increases, the number of hours of sleep (y - axis) decreases. For a linear function \(y = mx + b\), when \(m<0\), the function is decreasing. A quadratic function has the form \(y=ax^{2}+bx + c\). The scatter - plot does not show a parabolic (U - shaped or inverted U - shaped) pattern.

Answer:

C. Decreasing linear