How to find the average rate of change of a modeling function from a table | Khan Academy

TL;DR

The video explains how to calculate the rate of temperature change in Windhoek, Namibia, and compares the rates of increase between different time intervals.

Transcript

Let T of T, so capital T of lowercase T denote the temperature capital T in Windhoek, Namibia measured in degrees Celsius when it's T lowercase T hours after midnight on a given day. The table below lists a few selected values of the function. Alright, when it's 6 hours after midnight our temperature is 19 degrees Celsius Nine hours after midnight ... Read More

Key Insights

• 💱 Temperature changes in Windhoek, Namibia, can be analyzed using rates of temperature change.
• 💱 Calculating the rate of temperature change involves dividing the change in temperature by the change in time.
• ☠️ The rate of temperature increase can vary between different time intervals.
• ☠️ The interval between 6am and 9am had a faster rate of temperature increase compared to 9am and 1pm.

Questions & Answers

Q: How can we calculate the rate of temperature change?

The rate of temperature change can be calculated by dividing the change in temperature by the change in time. It gives us an average rate per unit of time, such as degrees Celsius per hour.

Q: What was the rate of temperature change between 6am and 9am?

The temperature increased by 6 degrees Celsius over 3 hours, giving us a rate of change of 2 degrees Celsius per hour.

Q: What was the rate of temperature change between 9am and 1pm?

The temperature increased by 6 degrees Celsius over 4 hours, resulting in a rate of change of 1.5 degrees Celsius per hour.

Q: Which interval had a faster rate of temperature increase?

The interval between 6am and 9am had a faster rate of temperature increase with 2 degrees Celsius per hour, compared to 1.5 degrees Celsius per hour between 9am and 1pm.

Summary & Key Takeaways

• The video discusses the temperature changes in Windhoek, Namibia, at different hours after midnight.

• It calculates the rate of temperature change by dividing the change in temperature by the change in time.

• It compares the rates of increase between the time intervals of 6am-9am and 9am-1pm.