How to estimate the average rate of change of a modeling function from a graph | Khan Academy | Summary and Q&A

TL;DR

Teresa's height decreases at a varying rate as time progresses, with a significant decrease when she deploys the parachute.

Key Insights

• ⌛ Teresa's height decreases as time progresses during the skydiving experience.
• ☠️ The rate of decline in her height is steeper as time approaches 10 seconds after the jump.
• 🥺 Teresa deploys the parachute at 10 seconds, leading to a slower rate of decline in her height.
• ⌛ The graph represents Teresa's height as a function of time, measured in seconds.
• 🤒 The average rate of change of Teresa's height between 3 seconds and 8 seconds is approximately -55 meters per second.
• ☠️ It is important to consider the negative sign when interpreting the average rate of change as a decrease in height.
• 🤒 The approximate height at 3 seconds is 650 meters, and at 8 seconds, it is approximately 375 meters.

Transcript

Teresa went skydiving. The graph below discribes Teresa's height, measured in meters, as a function of time, measured in seconds. So let's look at this graph over here. It's actually quite large, so let me zoom out a little bit. And we can see that at time zero her height is seven hundred meters and then as time increases, as we move to the right h... Read More

Questions & Answers

Q: What is the initial height of Teresa when she jumps?

Teresa's height is 700 meters when she first jumps from the plane.

Q: How does Teresa's rate of height decline change with time?

As time progresses, Teresa's rate of height decline becomes faster until she deploys the parachute. After deploying the parachute, her rate of decline slows down.

Q: What is Teresa's height at 3 seconds and 8 seconds after the jump?

At 3 seconds, Teresa's height is approximately 650 meters, and at 8 seconds, her height is approximately 375 meters.

Q: What is the average rate of change in Teresa's height between 3 seconds and 8 seconds?

The average rate of change in Teresa's height between 3 seconds and 8 seconds is approximately -55 meters per second, indicating a decrease in height.

Summary & Key Takeaways

• Teresa's height starts at 700 meters and decreases over time.

• The rate of decline in her height becomes steeper as time progresses until she deploys the parachute.

• After deploying the parachute, her rate of decline slows down.