Exponential Growth & Decay

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What is Exponential Growth?

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Exponential Growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase. Example: A population that grows by 10% each year.

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What is Exponential Decay?

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Exponential Decay occurs when a quantity decreases by a consistent percentage over time, leading to a rapid decrease. Example: A radioactive substance that decays by 5% each year.

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What is the formula for Exponential Growth?

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The formula is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

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What is the formula for Exponential Decay?

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The formula is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

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How do you calculate the population after a percentage decrease?

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Use the formula: Final Population = Initial Population × (1 - Decay Rate)^t.

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What is a Growth Factor?

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The Growth Factor is the multiplier used in exponential growth, calculated as (1 + growth rate). Example: For a 60% increase, the growth factor is 1.6.

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What is a Decay Factor?

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The Decay Factor is the multiplier used in exponential decay, calculated as (1 - decay rate). Example: For a 4.5% decrease, the decay factor is 0.955.

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What does a graph of Exponential Growth look like?

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A graph of Exponential Growth shows a curve that rises steeply as time increases, indicating rapid growth.

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What does a graph of Exponential Decay look like?

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A graph of Exponential Decay shows a curve that falls steeply as time increases, indicating rapid decrease.

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How do you identify Exponential Growth vs. Decay from a graph?

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If the graph rises sharply, it indicates Exponential Growth. If it falls sharply, it indicates Exponential Decay.