Algebra 1: Unit 3: Chapter 7: Exponents and Exponential Functions

exponential function

A function that can be described by an equation of the form y = a^x, where a > 0 and a ≠ 0.

constant

A monomial that is a real number.

scientific notation

A number in scientific notation is expressed as a x 10^n, where 1 ≤ a < 0 and n is an integer.

monomial

A number, a variable, or a product of a number and one or more variables.

geometric sequence

A sequence in which each term after the first is found by multiplying the previous term by a constant r, called the common ratio.

compound interest

A special application of exponential growth.

exponential equation

An equation in which the variables occur as exponents.

recursive formula

Each term is formulated from one or more previous terms.

zero exponent

For any nonzero number a, a^0 = 1; any nonzero number raised to the zero power is equal to 1.

rational exponent

For any positive real b and any integers m and n > 1, b(m/n) = (n√b)^m or n√b^m.

negative exponent

For any real number a ≠ 0 and any integer n, a^-n = 1/a^n and 1/a^-n = a^n.

exponential decay function

Functions of the form y = ab^x, where a > 0 and 0 < b < 1.

exponential growth function

Functions of the form y = ab^x, where a > 0, b < 1.

cube root

If a^3 = b, then a is the cube root of b.

nth root

If a^n = b for a positive integer n, then a is an nth root of b.

order of magnitude

The order of magnitude of a quantity is the number rounded to the nearest power of 10.

common ratio

The ratio of successive terms of a geometric sequence.