AFDA Exponential Growth and Decay

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What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a consistent percentage over a period of time, leading to rapid growth. Example: A population of bacteria doubles every hour.

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What is Exponential Decay?

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Exponential Decay occurs when a quantity decreases by a consistent percentage over a period of time. Example: A radioactive substance decreases by 5% each hour.

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What is the general formula for Exponential Growth?

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A = A₀(1 + r)ⁿ, where A₀ is the initial amount, r is the growth rate, and n is the number of time periods.

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What is the general formula for Exponential Decay?

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A = A₀(1 - r)ⁿ, where A₀ is the initial amount, r is the decay rate, and n is the number of time periods.

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What does the variable 'A' represent in exponential functions?

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In exponential functions, 'A' represents the amount after time 'n' has passed.

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What does the variable 'A₀' represent in exponential functions?

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A₀ represents the initial amount or starting value before any growth or decay occurs.

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What is an asymptote in the context of exponential functions?

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An asymptote is a line that a graph approaches but never touches. For exponential decay, the horizontal asymptote is typically y = 0.

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How can you identify Exponential Growth from a function?

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If the base of the exponential function is greater than 1 (e.g., A = 1200(1.05)ⁿ), it indicates Exponential Growth.

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How can you identify Exponential Decay from a function?

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If the base of the exponential function is between 0 and 1 (e.g., A = 1200(0.85)ⁿ), it indicates Exponential Decay.

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What is the significance of the growth/decay rate 'r'?

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The growth/decay rate 'r' indicates the percentage increase or decrease per time period.