Exponential Growth and Decay

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What is exponential growth?

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Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at a rate that becomes faster as the quantity increases.

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What is exponential decay?

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Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

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How do you calculate the future value of an investment with compound interest?

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The future value (FV) can be calculated using the formula: FV = P(1 + r)^t, where P is the principal amount, r is the annual interest rate, and t is the number of years.

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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 y is the final amount, 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 for exponential decay is y = a(1 - r)^t, where y is the final amount, a is the initial amount, r is the decay rate, and t is time.

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How do you convert a percentage increase to a growth factor?

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To convert a percentage increase to a growth factor, add 1 to the percentage expressed as a decimal. For example, a 20% increase becomes 1 + 0.20 = 1.20.

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How do you convert a percentage decrease to a decay factor?

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To convert a percentage decrease to a decay factor, subtract the percentage expressed as a decimal from 1. For example, a 15% decrease becomes 1 - 0.15 = 0.85.

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What is the significance of the base 'e' in exponential functions?

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The base 'e' (approximately 2.718) is significant in exponential functions as it represents continuous growth or decay, commonly used in natural processes and financial calculations.

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What is the difference between linear and exponential growth?

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

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How can you determine the time it takes for an investment to double using the Rule of 72?

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The Rule of 72 states that you can estimate the number of years required to double an investment by dividing 72 by the annual interest rate (in percentage).