Introduction to exponential decay

TL;DR

This video explains the concepts of exponential growth and exponential decay using tables, equations, and graphs.

Transcript

• [Narrator] What we're going to do in this video is quickly review exponential growth and then use that as our platform to introduce ourselves to exponential decay. So let's review exponential growth. Let's say we have something that, and I'll do this on a table here. Just gonna make that straight. So let's say this is our x and this is our y. Now... Read More

Key Insights

• ‼️ Exponential growth occurs when a quantity doubles or increases by a constant ratio as x increases.
• 🥳 The equation for exponential growth is y = A * (r^x), where A is the initial value and r is the common ratio.
• ☺️ Exponential decay involves a quantity shrinking or decreasing by a constant ratio as x increases.
• 😀 The equation for exponential decay is also y = A * (r^x), but with the absolute value of r less than 1.
• 🛀 Both exponential growth and decay can be graphed, with growth showing a curve that approaches positive infinity and decay approaching zero.
• 📈 Exponential growth and decay can be represented by tables, equations, and graphs.
• 🥳 The common ratio determines the rate of growth or decay.

Questions & Answers

Q: What is the equation for exponential growth?

The equation for exponential growth is y = A * (r^x), where A represents the initial value, and r is the common ratio.

Q: How can exponential growth be represented on a graph?

Exponential growth is represented by a curve that increases rapidly as x increases. The curve will approach positive infinity but never reach it.

Q: Explain exponential decay and its equation.

Exponential decay involves a quantity decreasing by a constant ratio as x increases. The equation for exponential decay is y = A * (r^x), where the absolute value of r is less than 1.

Q: What does the graph of exponential decay look like?

The graph of exponential decay shows a curve that decreases rapidly as x increases. The curve approaches the x-axis but never reaches it.

Summary & Key Takeaways

• The video begins by reviewing exponential growth, where a quantity doubles or increases by a constant ratio as x increases. This can be represented by the equation y = A * (r^x).

• Exponential decay, on the other hand, involves a quantity shrinking or decreasing by a constant ratio as x increases. The equation for exponential decay is y = A * (r^x), where the absolute value of r is less than 1.

• Both exponential growth and decay can be graphed, with growth showing a curve that approaches positive infinity as x increases, and decay showing a curve that approaches zero as x increases.