Which Graph Represents Exponential Decay?
Exponential decay is a type of function that decreases at an increasing rate. The graph of an exponential decay function is always concave down, and it approaches a horizontal asymptote as x approaches infinity.
To determine which graph represents exponential decay, there are a few things to look for:
- The graph should be concave down. This means that the curve should curve downwards as x increases.
- The graph should approach a horizontal asymptote as x approaches infinity. This means that the graph should get closer and closer to a horizontal line as x gets larger and larger.
Here are some examples of graphs that represent exponential decay:
- The graph of y = e^(-x). This graph is concave down and approaches the horizontal asymptote y = 0 as x approaches infinity.
- The graph of y = 1/(x + 1). This graph is also concave down and approaches the horizontal asymptote y = 0 as x approaches infinity.
Here are some questions that can be used to determine which graph represents exponential decay:
- Does the graph curve downwards as x increases?
- Does the graph approach a horizontal asymptote as x approaches infinity?
If the answer to both of these questions is yes, then the graph represents exponential decay.
Here are some additional questions that can be asked to further clarify the situation:
- What is the horizontal asymptote of the graph?
- What is the initial value of the graph?
These questions can help to identify the specific function that is represented by the graph.
Example 1
Consider the following two graphs:
[Image of Graph 1] [Image of Graph 2]Which graph represents exponential decay?
Answer:
Graph 2 represents exponential decay. This is because graph 2 is concave down and approaches the horizontal asymptote y = 0 as x approaches infinity.
Example 2
Consider the following graph:
[Image of Graph 3]Does this graph represent exponential decay?
Answer:
No, this graph does not represent exponential decay. This is because the graph is concave up, which means that it curves upwards as x increases. Additionally, the graph does not approach a horizontal asymptote as x approaches infinity.
In conclusion, to determine which graph represents exponential decay, look for a graph that is concave down and approaches a horizontal asymptote as x approaches infinity.