Question

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	hours of sleep
6	30
9	45
12	60
15	75

what is the rate of change of waynes hours of sleep with respect to each day?

a. 5 hours per day
b. 6 hours per day
c. 8 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 \(\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Choose two points from the table

Let's take the first two points: \((3, 15)\) and \((6, 30)\).

Step3: Calculate the rate of change

Substitute into the formula: \(\frac{30 - 15}{6 - 3}=\frac{15}{3} = 5\). We can check with other points, e.g., \((6, 30)\) and \((9, 45)\): \(\frac{45 - 30}{9 - 6}=\frac{15}{3}=5\). So the rate is consistent.

Answer:

A. 5 hours per day