Math Problem Statement
Solution
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 increases. This happens for functions of the form , where and , or more generally for forms like where .
Now, let's analyze the graphs in your image:
- Graph 1 (Top graph): This is a linear graph, not exponential, as it shows a straight line.
- Graph 2 (Second from the top): This graph increases slowly, indicating it might represent exponential growth, not decay.
- Graph 3 (Third graph): This graph starts high and decreases rapidly, flattening out as increases. This matches the behavior of exponential decay.
- 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:
- What is the general form of an exponential decay function?
- How can you differentiate between exponential growth and decay by looking at their graphs?
- What are the real-world applications of exponential decay?
- Can exponential decay functions ever reach zero?
- 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.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Exponential Functions
Graph Analysis
Formulas
y = a e^{-kx}, a > 0, k > 0
y = a (1/b)^x, 0 < b < 1
Theorems
Exponential Decay
Suitable Grade Level
Grades 9-12