Exponential functions are a fundamental concept in Algebra 2. They describe relationships where a quantity increases or decreases at a constant percentage rate over time. The general form of an exponential function is $f(x) = ab^x$, where $a$ is the initial value, $b$ is the growth/decay factor, and $x$ is the independent variable (often time). Evaluating exponential functions involves substituting a given value for $x$ and calculating the corresponding value of $f(x)$.
Understanding how to evaluate these functions is crucial for solving real-world problems related to population growth, compound interest, radioactive decay, and more. This quiz will provide practice in evaluating exponential functions for different values of $x$ and with varying parameters for $a$ and $b$.
Match the following terms with their definitions:
| Term | Definition |
|---|---|
| 1. Exponential Function | A. The factor by which a quantity changes. |
| 2. Initial Value | B. A function of the form $f(x) = ab^x$. |
| 3. Growth Factor | C. The value of the function when $x = 0$. |
| 4. Decay Factor | D. When the value of b is between 0 and 1. |
| 5. Asymptote | E. A line that a curve approaches but never touches. |
Complete the following paragraph with the correct terms:
An exponential function has the form $f(x) = ab^x$, where '$a$' represents the ________, '$b$' is the ________, and '$x$' is the ________. If $b > 1$, the function represents exponential ________. If $0 < b < 1$, it represents exponential ________.
Explain, in your own words, how changing the value of 'a' and 'b' in an exponential function affects its graph. Provide examples to support your explanation.
Please log in to post your answer.
Log InEarn 2 Points for answering. If your answer is selected as the best, you'll get +20 Points! 🚀