Questions and Answers
What is the common ratio in a geometric sequence?
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 $b$.
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What is exponential decay?
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What defines an exponential equation?
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What is an exponential function?
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What is exponential growth?
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Define a geometric sequence.
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What is a monomial?
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What is a negative exponent?
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Define nth root.
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What does order of magnitude mean?
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What is a rational exponent?
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What is a recursive formula?
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What is scientific notation?
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What does zero exponent signify?
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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.