Question

the graph represents a joggers speed during her jog around her neighborhood. over which interval did her speed increase most quickly? her speed increased most quickly between
and
minutes.
graphing calculator

Explanation:

Step1: Identify speed change intervals

First, list all intervals where speed increases:

• 0 to 3 min: Speed from 0 to 3 mph
• 5 to 7 min: Speed from 3 to 5 mph
• 7 to 9 min: Speed from 5 to 7 mph
• 9 to 10 min: Speed from 7 to 8 mph
• 12 to 14 min: Speed from 8 to 12 mph
• 16 to 19 min: Speed from 12 to 18 mph

Step2: Calculate rate of increase

Rate = $\frac{\text{Change in Speed}}{\text{Change in Time}}$

• 0-3: $\frac{3-0}{3-0}=1$ mph/min
• 5-7: $\frac{5-3}{7-5}=1$ mph/min
• 7-9: $\frac{7-5}{9-7}=1$ mph/min
• 9-10: $\frac{8-7}{10-9}=1$ mph/min
• 12-14: $\frac{12-8}{14-12}=2$ mph/min
• 16-19: $\frac{18-12}{19-16}=2$ mph/min

Step3: Compare all rates

The highest rate is 2 mph/min, occurring in two intervals. The question asks for one interval; the earlier or either valid interval works, and 12 to 14 is a clear valid interval.

Answer:

Her speed increased most quickly between 12 and 14 minutes.