Exponential Growth & Decay

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What is exponential growth?

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Exponential growth occurs when the increase in a quantity is proportional to its current value, leading to growth at an increasing rate. For example, if a population doubles every fixed period, it is experiencing exponential growth.

Tags

CCSS.HSF-LE.A.1A

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What is exponential decay?

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Exponential decay is the decrease in a quantity at a rate proportional to its current value, resulting in a rapid decline. An example is radioactive decay, where the amount of substance decreases over time.

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CCSS.HSF-IF.C.8B

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How do you calculate the future value in exponential growth?

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The formula is: Future Value = Present Value × (1 + growth rate)^number of periods.

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CCSS.HSF-IF.C.8B

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How do you calculate the future value in exponential decay?

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The formula is: Future Value = Present Value × (1 - decay rate)^number of periods.

Tags

CCSS.HSF-IF.C.8B

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What is the formula for continuous exponential growth?

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The formula is: A = Pe^(rt), where A is the amount after time t, P is the initial amount, r is the growth rate, and e is Euler's number (approximately 2.718).

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What is the formula for continuous exponential decay?

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The formula is: A = Pe^(-rt), where A is the amount after time t, P is the initial amount, r is the decay rate, and e is Euler's number.

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If a population of 1000 doubles every 3 years, what will it be after 9 years?

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After 9 years, the population will be 8000 (1000 × 2^3).

Tags

CCSS.HSF.LE.A.4

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What is the half-life in the context of exponential decay?

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Half-life is the time required for a quantity to reduce to half its initial value. It is a key concept in radioactive decay and other decay processes.

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How does a percentage decrease affect a population?

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A percentage decrease reduces the population by that percentage each period. For example, a 10% decrease means the population is multiplied by 0.90 each period.

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CCSS.HSF.BF.A.2

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What is the difference between linear and exponential growth?

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Linear growth increases by a constant amount, while exponential growth increases by a percentage of the current amount, leading to faster growth over time.