Glencoe Algebra 1 Chapter 7 Vocabulary

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Questions and Answers

What is the common ratio in a geometric sequence?

The ratio of successive terms (correct)

The sum of terms

The first term

The product of terms

What is compound interest?

A special application of exponential growth

What is a constant in mathematics?

A monomial that is a real number

If $a^3=b$, then $a$ is the ________ of $b$.

cube root Signup and view all the answers

What is exponential decay?

When an initial amount decreases by the same percent over a given period of time Signup and view all the answers

What defines an exponential equation?

An equation in which the variables occur as exponents Signup and view all the answers

What is an exponential function?

A function that can be described by an equation of the form $y=a^x$, where $a>0$ and $a$ does not equal 1 Signup and view all the answers

What is exponential growth?

When an initial amount increases by the same percent over a given period of time Signup and view all the answers

Define a 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 Signup and view all the answers

What is a monomial?

A number, variable, or a product of a number and one or more variables Signup and view all the answers

What is a negative exponent?

For any real number $a$ not equal to 0 and any integer $n$, $a^{-n} = 1/a^n$ and $1/a^{-n} = a^n$ Signup and view all the answers

Define nth root.

If $a^n = b$ for a positive integer $n$, then $a$ is an nth root of $b$ Signup and view all the answers

What does order of magnitude mean?

The order of magnitude of a quantity is the number rounded to the nearest power of 10 Signup and view all the answers

What is a rational exponent?

For any positive real number $b$ and any integers $m$ and $n > 1$, $b^{m/n} = (n$ square root $b)^m$ or $n$ square root $b^{m/n}$ Signup and view all the answers

What is a recursive formula?

Each term is formulated from one or more previous terms Signup and view all the answers

What is scientific notation?

A number in scientific notation is expressed as $a * 10^n$ where $1 \leq a < 10$ and $n$ is an integer Signup and view all the answers

What does zero exponent signify?

For any nonzero number $a$, $a^0 = 1$; any nonzero number raised to the zero power is equal to 1 Signup and view all the answers

Study Notes

Geometric and Exponential Concepts

Common Ratio: Essential in geometric sequences, derived from the ratio of successive terms.
Geometric Sequence: Each term after the first is obtained by multiplying the previous term by a constant, termed the common ratio.
Exponential Growth: Characterized by an initial amount increasing by a consistent percentage over time.
Exponential Decay: Defined by an initial amount that decreases by the same percentage across a specified duration.

Mathematical Definitions

Compound Interest: A practical application of exponential growth, calculating interest over time on both the initial principal and accumulated interest.
Exponential Function: Represented by the equation y = a^x, where a (base) is positive and not equal to 1.
Exponential Equation: Contains variables that function as exponents, often requiring specific methods to solve.

Roots and Exponents

Cube Root: For an equation of the form a^3 = b, a is identified as the cube root of b.
Nth Root: Generalizes root extraction; if a^n = b with n as a positive integer, then a is the nth root of b.
Negative Exponent: Defined by a^-n = 1/a^n; it signifies the reciprocal relationship of the base when raised to a negative power.
Zero Exponent: Any non-zero number raised to the zero power equals 1, a foundational property in exponent rules.
Rational Exponent: Expressing roots using fractions; for instance, b^(m/n) correlates to the nth root of b raised to the m power.

Basic Algebraic Structures

Constant: A real number independent of variables; acting as a monomial in algebraic expressions.
Monomial: A single term comprising a number, variable, or a combination of both, helping build polynomial expressions.

Measurement and Representation

Order of Magnitude: Represents the scale of a quantity, rounded to the nearest power of 10, providing insight into its size.
Scientific Notation: A method of expressing numbers in the form a * 10^n, where 1 ≤ a < 10 and n is an integer, streamlining the representation of large or small numbers.

Recursive Processes

Recursive Formula: Formulates terms based on prior terms, key in constructing sequences or series.

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Description

Test your knowledge of key vocabulary from Chapter 7 of Glencoe Algebra 1. This quiz focuses on important terms related to geometric sequences, exponential growth, and more. Perfect for reinforcing your understanding of algebra concepts.