Applied rate of change: forgetfulness | Applications of derivatives | AP Calculus AB | Khan Academy

TL;DR

The video explains how to calculate the rate of change of the number of known words per day, using a given equation.

Transcript

I studied for an English test today and learned 80 vocabulary words. In 10 days, I will have forgotten every word. The number of words that I remember t days after studying is modeled by-- so W of t, so this is the number of words I have in my head as a function of time is going to be equal to 80 times 1 minus 0.1t squared for t is between 0 and 10... Read More

Key Insights

• 🏆 The equation W(t) = 80(1 - 0.1t^2) models the number of known words after studying for a test.
• ☠️ The rate of change of the number of known words can be found by taking the derivative of the equation.
• ⌛ Evaluating the derivative at a specific time point gives the rate of change at that time.
• 🥳 The negative rate of change implies a decrease in the number of known words per day.

Questions & Answers

Q: How can the number of known words be modeled after studying?

The number of known words can be modeled using the equation W(t) = 80(1 - 0.1t^2), where t is the number of days since studying.

Q: How can the rate of change of the number of known words be found?

The rate of change can be found by taking the derivative of the equation W(t) = 80(1 - 0.1t^2) with respect to time.

Q: What is the derivative of 1 - 0.1t^2?

The derivative of 1 - 0.1t^2 is 2(1 - 0.1t)(-0.1).

Q: What does the negative rate of change imply?

The negative rate of change (-12.8 words per day) implies that the number of known words is decreasing by 12.8 words every day.

Summary & Key Takeaways

• The video introduces an equation that models the number of words retained in the brain after studying for a test.

• The rate of change of the number of known words per day can be calculated by taking the derivative of the equation with respect to time.

• By evaluating the derivative at a specific time point, the rate of change can be determined.