Question

t = 0 s, 8 items eaten t = 4 s, 6 items eaten which phrase describes what is happening in this graph? a negative amount is eaten. a changing amount is eaten. a constant amount is eaten. nothing is consumed.

Explanation:

Step1: Calculate the rate of change

The rate of change formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \(x_1 = 0\), \(y_1=8\), \(x_2 = 4\), \(y_2 = 6\). Then \(m=\frac{6 - 8}{4-0}=\frac{-2}{4}=-\frac{1}{2}\).

Step2: Analyze the meaning of the rate of change

Since the rate of change \(m =-\frac{1}{2}
eq0\), the amount eaten is changing. A negative rate of change means the amount is decreasing over time.

Answer:

A changing amount is eaten.