Exponents and Exponential Expressions
Exponentiation is a basic operation that indicates how many times a number is multiplied by itself. If a is a number and n is an integer, then aⁿ is the power.
Basic Identities
Negative and Fractional Exponents
The concept of exponents can be extended to negative and fractional exponents as well.
- Negative exponent:
- Fractional exponent:
- In general:
Exponential Functions
Exponential functions are of the form where the variable is in the exponent. The most well-known is f(x) = a^x, where a > 0 and a ≠ 1.
If 0 < a < 1, the function is decreasing. If a > 1, it is increasing. This makes exponential functions extremely important in natural and social sciences.
Examples
- Compound interest calculation:
- Bacteria reproduction at an exponential rate.
Practice Exercise
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