Exponential Growth and 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. It can be modeled by the equation 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 exponential decay?

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Exponential decay is the process by which a quantity decreases at a rate proportional to its current value. It can be modeled by the equation y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

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What is the decay factor?

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The decay factor is the multiplier used in exponential decay equations, calculated as (1 - decay rate). For example, if the decay rate is 20%, the decay factor is 0.8.

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What is the growth factor?

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The growth factor is the multiplier used in exponential growth equations, calculated as (1 + growth rate). For example, if the growth rate is 80%, the growth factor is 1.8.

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How do you calculate the remaining amount after exponential decay?

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To calculate the remaining amount after exponential decay, use the formula y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is the time.

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How do you calculate the remaining amount after exponential growth?

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To calculate the remaining amount after exponential growth, use the formula y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is the time.

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If a substance decays by 20% per hour, what is the decay factor?

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The decay factor is 0.8, calculated as (1 - 0.2).

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If a substance grows by 80%, what is the growth factor?

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The growth factor is 1.8, calculated as (1 + 0.8).

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What is the formula for exponential decay?

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The formula for exponential decay 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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What is the formula for exponential growth?

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