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 over time.

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What is the formula for Exponential Growth?

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The formula is: P(t) = P0 * (1 + r)^t, where P(t) is the future population, P0 is the initial population, r is the growth rate, and t is time.

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What is Exponential Decay?

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Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to a decrease at a decreasing rate over time.

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What is the formula for Exponential Decay?

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The formula is: P(t) = P0 * (1 - r)^t, where P(t) is the future value, P0 is the initial value, r is the decay rate, and t is time.

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What is a Growth Factor?

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The growth factor is the amount by which a quantity increases in one time period, calculated as (1 + r) for growth.

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What is a Decay Factor?

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The decay factor is the amount by which a quantity decreases in one time period, calculated as (1 - r) for decay.

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How do you calculate the future value of an investment with exponential growth?

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Use the formula: Future Value = Present Value * (1 + growth rate)^number of periods.

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How do you calculate the future value of an investment with exponential decay?

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Use the formula: Future Value = Present Value * (1 - decay rate)^number of periods.

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What is the significance of the rate in exponential functions?

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The rate determines how quickly the quantity grows or decays; a higher rate results in faster changes.

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How does compounding affect exponential growth?

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Compounding leads to exponential growth because the growth builds on itself, increasing the base amount each period.