https://file.aiquickdraw.com/mathbot/file/1727301652549hj5dtwcm.jpg

To determine which graph represents exponential decay, let's quickly define it: **Exponential decay** is when a function decreases rapidly at first, then levels off toward zero as \( x \) increases. This happens for functions of the form \( y = a e^{-kx} \), where \( a > 0 \) and \( k > 0 \), or more generally for forms like \( y = a \left(\frac{1}{b}\right)^x \) where \( 0 < b < 1 \).

Now, let's analyze the graphs in your image:

1. **Graph 1 (Top graph):** This is a linear graph, not exponential, as it shows a straight line.
2. **Graph 2 (Second from the top):** This graph increases slowly, indicating it might represent **exponential growth**, not decay.
3. **Graph 3 (Third graph):** This graph starts high and decreases rapidly, flattening out as \( x \) increases. This matches the behavior of **exponential decay**.
4. **Graph 4 (Bottom graph):** This is also an increasing curve, suggesting it represents **exponential growth**.

Therefore, **Graph 3** (third from the top) represents **exponential decay**.

Would you like further details or explanations?

Here are 5 questions to deepen your understanding:
1. What is the general form of an exponential decay function?
2. How can you differentiate between exponential growth and decay by looking at their graphs?
3. What are the real-world applications of exponential decay?
4. Can exponential decay functions ever reach zero?
5. How does the rate of decay change as the value of the exponent increases?

**Tip:** Exponential decay is characterized by a base between 0 and 1, while growth has a base greater than 1.

Which graph represents exponential decay?

Learn how to identify graphs representing exponential decay by analyzing the behavior of different functions. This problem covers key concepts in exponential functions and graph interpretation. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation