Question

select the correct answer. wayne is recording the number of hours he sleeps over different periods of time. the table provided shows the number of hours wayne sleeps during the respective amount of days.
number of days | 3 | 6 | 9 | 12 | 15
hours of sleep | 15 | 30 | 45 | 60 | 75
what is the rate of change of wayne’s hours of sleep with respect to each day?
a. 6 hours per day
b. 8 hours per day
c. 3 hours per day
d. 5 hours per day

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x\) is the number of days and \(y\) is hours of sleep. Let's take two points, e.g., \((3, 15)\) and \((6, 30)\).

Step2: Calculate rate of change

Using the formula: \(\frac{30 - 15}{6 - 3}=\frac{15}{3} = 5\). We can check with another pair, like \((6, 30)\) and \((9, 45)\): \(\frac{45 - 30}{9 - 6}=\frac{15}{3}=5\). So the rate of change is 5 hours per day.

Answer:

D. 5 hours per day