Exponent

Definition

An exponent indicates how many times a number, known as the base, is multiplied by itself. It is typically represented as a small number to the upper right of the base.

5 Must Know Facts For Your Next Test

1. The general form of an exponential function is $f(x) = a \cdot b^x$, where $a$ and $b$ are constants.
2. Exponential growth occurs when the base $b > 1$, while exponential decay occurs when $0 < b < 1$.
3. The natural exponential function has the base $e \approx 2.718$, denoted as $f(x) = e^x$.
4. Properties of exponents include: $a^m \cdot a^n = a^{m+n}$ and $(a^m)^n = a^{mn}$.
5. Exponential functions have horizontal asymptotes, usually along the x-axis or y-axis depending on transformations.

Review Questions

• What is the base in the exponential function $3 \cdot 2^x$?
• Determine whether the function $f(x) = (1/3)^x$ represents growth or decay.
• Explain why $e$ is used as a base in natural exponential functions.

Related terms

Base: The number that is raised to a power by an exponent, e.g., in $2^3$, 2 is the base.

Natural Exponential Function: $f(x) = e^x$, where $e$ is Euler's number, approximately equal to 2.718.

Logarithm: The inverse operation to exponentiation, indicating what power a base must be raised to obtain a given number.