Exponential graphs represent relationships where a quantity increases or decreases at a constant percentage rate over time. These graphs have a distinctive curved shape. Identifying key features like the y-intercept, asymptote, growth/decay factor, and domain/range is crucial for understanding the behavior of the exponential function they represent. Whether it's population growth, radioactive decay, or compound interest, exponential functions are everywhere!
Match each term with its correct definition:
| Term | Definition |
|---|---|
| 1. Asymptote | a) The initial value of the function when x = 0 |
| 2. Exponential Growth | b) A line that a curve approaches but never touches |
| 3. Exponential Decay | c) A function where the rate of increase slows down as x increases. |
| 4. Y-intercept | d) A function where the rate of increase quickens as x increases. |
| 5. Domain | e) The set of all possible input values (x-values) for a function |
Match the following: 1-b, 2-d, 3-c, 4-a, 5-e
Complete the following paragraph using the words provided:
(growth factor, horizontal, exponential, y-intercept, decay)
An ________ function is characterized by a constant ________. The _________ is the point where the graph crosses the y-axis. Exponential ______ occurs when the base of the exponential function is between 0 and 1. The asymptote in these graphs is typically ______.
Answer: exponential, growth factor, y-intercept, decay, horizontal
Describe a real-world scenario that can be modeled by an exponential graph. Explain what the axes represent and how the key features of the graph (y-intercept, asymptote, growth/decay) relate to the scenario.
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