Question

what is jadas fastest rate of change?
height (cm)
time (minutes)

Explanation:

Step1: Identify line segments

The graph has 4 segments: (0,0)-(2,10), (2,10)-(3,10), (3,10)-(5,30), (5,30)-(7,25), (7,25)-(10,25)

Step2: Calculate rate for segment 1

Rate = $\frac{\Delta \text{height}}{\Delta \text{time}} = \frac{10-0}{2-0} = 5$ cm/min

Step3: Calculate rate for segment 2

Rate = $\frac{\Delta \text{height}}{\Delta \text{time}} = \frac{10-10}{3-2} = 0$ cm/min

Step4: Calculate rate for segment 3

Rate = $\frac{\Delta \text{height}}{\Delta \text{time}} = \frac{30-10}{5-3} = 10$ cm/min

Step5: Calculate rate for segment 4

Rate = $\frac{\Delta \text{height}}{\Delta \text{time}} = \frac{25-30}{7-5} = -2.5$ cm/min

Step6: Calculate rate for segment 5

Rate = $\frac{\Delta \text{height}}{\Delta \text{time}} = \frac{25-25}{10-7} = 0$ cm/min

Step7: Compare absolute rates

Absolute values: 5, 0, 10, 2.5, 0. The largest is 10.

Answer:

10 cm per minute