Exponents And Powers Study Cards

Enhance Your Learning with Exponents and Powers Flash Cards for quick learning



Exponent

A number that represents the power to which another number, called the base, is raised.

Base

The number that is raised to a power.

Power

The result of raising a base to an exponent.

Product of Powers

When multiplying powers with the same base, add the exponents.

Quotient of Powers

When dividing powers with the same base, subtract the exponents.

Power of a Power

When raising a power to another power, multiply the exponents.

Zero Exponent

Any nonzero number raised to the power of zero is equal to 1.

Negative Exponent

A negative exponent indicates the reciprocal of the base raised to the positive exponent.

Scientific Notation

A way of expressing numbers that are too large or too small to be conveniently written in decimal form.

Exponential Growth

A pattern of growth where the quantity increases by a fixed percentage over a fixed time period.

Exponential Decay

A pattern of decay where the quantity decreases by a fixed percentage over a fixed time period.

Powers of Ten

Numbers that can be expressed as a product of a power of 10 and a decimal number greater than or equal to 1 and less than 10.

Radical

The symbol √ used to indicate the square root of a number.

Rational Exponent

An exponent that can be expressed as a fraction.

Logarithm

The inverse operation of exponentiation. It gives the power to which a base must be raised to obtain a given number.

Common Logarithm

A logarithm with base 10.

Natural Logarithm

A logarithm with base e, where e is the mathematical constant approximately equal to 2.71828.

Change of Base Formula

A formula used to evaluate logarithms with bases other than 10 or e.

Logarithmic Properties

Various properties and rules that can be used to simplify logarithmic expressions.

Exponential Equations

Equations in which the variable appears in the exponent.

Logarithmic Equations

Equations in which the variable appears inside a logarithm.

Exponential Growth Formula

A formula used to model exponential growth: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Exponential Decay Formula

A formula used to model exponential decay: A = P(1 - r/n)^(nt), where A is the final amount, P is the initial amount, r is the decay rate, n is the number of times decay occurs per year, and t is the number of years.

Half-Life

The time it takes for half of a substance to decay or for the quantity to decrease by half.

Compound Interest

Interest that is calculated on the initial principal and also on the accumulated interest of previous periods.

Continuous Compound Interest

Interest that is compounded continuously, resulting in an exponential growth formula: A = Pe^(rt), where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the number of years.

Exponential Function

A function of the form f(x) = a * b^x, where a and b are constants and b is the base of the exponential function.

Exponential Decay Function

A function of the form f(x) = a * b^(-x), where a and b are constants and b is the base of the exponential function.

Exponential Growth Function

A function of the form f(x) = a * b^x, where a and b are constants and b is greater than 1.

Exponential Regression

A statistical method used to model data that exhibits exponential growth or decay.

Exponential Smoothing

A forecasting technique that uses a weighted average of past observations to predict future values, with more weight given to recent observations.

Exponential Distribution

A probability distribution that describes the time between events in a Poisson process, where events occur continuously and independently at a constant average rate.

Exponential Growth Rate

The rate at which a quantity increases exponentially over time.

Exponential Decay Rate

The rate at which a quantity decreases exponentially over time.

Exponential Time Complexity

A measure of the efficiency of an algorithm, indicating that the running time of the algorithm increases exponentially with the size of the input.

Exponential Notation

A way of expressing a number as a product of a coefficient and a power of 10.

Exponential Moving Average

A statistical calculation used to analyze data trends by smoothing out fluctuations and highlighting long-term patterns.

Exponential Decay Factor

The factor by which a quantity decreases exponentially over time.

Exponential Growth Factor

The factor by which a quantity increases exponentially over time.

Exponential Distribution Function

A mathematical function that describes the probability distribution of a continuous random variable.