# Unit4Vocabulary Flashcards

Negative Exponent Property

a^{-b} = 1/a^{b}

Doubling Time

The time if takes for an exponential growth equation to double in value. Typically used in population and investment studies.

Exponent

The power a number is raised to.

__Ex__: a^{n} where n is the Exponent

Exponential Function

y = ab^{x}

Base e Log

Known as the Natural Log it can be written as log_{e} but is traditionally written as ln.

Rationalized Denominator

An expression that does not contain a radical in the denominator.

Depreciation

When the value of an object decreases by a percentage over a set period of time. Can be modeled by an exponential equation.

__Ex__: y = 75(1 - 0.23)^{x}

Quotient of Powers Property

Base 10 Log

Usually denoted by just log but can be written as log_{10}. It is the base used by calculators when accessing the log key.

Common Base Property

If a^{x} = a^{y}, then x = y

Half Life

The time if takes a radioactive substance to decay to half of its initial value.

Power of a Quotient Property

Exponential Growth

An exponential equation that increases as the input increases.

y = y_{0} (1 + r)^{x}

Logarithm

The inverse of an exponential function.

Given: a^{x} = b

Then: log_{a}b = x

What power of a equals b?

Exponential Decay

An exponential equation that decreases as the input increases.

y = y_{0} (1 - r)^{x}