Alg I-8 3A Review

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What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase. Example: If a population doubles every year, it is experiencing exponential growth.

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What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease. Example: If a radioactive substance loses half of its mass every year, it is experiencing exponential decay.

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What is an Arithmetic Sequence?

Back

An Arithmetic Sequence is a sequence of numbers in which the difference between consecutive terms is constant. Example: 2, 5, 8, 11 (the common difference is 3).

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What is a Geometric Sequence?

Back

A Geometric Sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. Example: 3, 6, 12, 24 (the common ratio is 2).

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How do you identify an Arithmetic Sequence?

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To identify an Arithmetic Sequence, check if the difference between consecutive terms is constant. If it is, then it is an arithmetic sequence.

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How do you identify a Geometric Sequence?

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To identify a Geometric Sequence, check if the ratio of consecutive terms is constant. If it is, then it is a geometric sequence.

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What is the formula for the nth term of an Arithmetic Sequence?

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The nth term of an Arithmetic Sequence can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

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What is the formula for the nth term of a Geometric Sequence?

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The nth term of a Geometric Sequence can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

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What is the difference between growth and decay in exponential functions?

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In exponential growth, the function increases over time, while in exponential decay, the function decreases over time.

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What does it mean if a sequence is neither arithmetic nor geometric?

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A sequence is neither arithmetic nor geometric if it does not have a constant difference (arithmetic) or a constant ratio (geometric) between its terms.