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, resulting in a rapid increase. Example: A population of bacteria doubles every hour.

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What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease. Example: A radioactive substance loses half of its mass every 5 years.

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What is the formula for Exponential Growth?

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The formula is A = P(1 + r)^t, where A is the amount after time t, P 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 A = P(1 - r)^t, where A is the amount after time t, P is the initial amount, r is the decay rate, and t is time.

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What does the base of an exponential function represent?

Back

The base represents the growth or decay factor. For growth, it is greater than 1; for decay, it is between 0 and 1.

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If a quantity doubles every week, what is the growth factor?

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The growth factor is 2.

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What is the decay factor if a quantity decreases by 8%?

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The decay factor is 0.92 (1 - 0.08).

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How do you calculate the value of an asset after depreciation?

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Use the formula: Future Value = Initial Value × (1 - decay rate)^number of years.

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What is the difference between linear and exponential growth?

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Linear growth increases by a fixed amount, while exponential growth increases by a percentage, leading to much larger values over time.

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What is a real-world example of exponential growth?

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A common example is population growth, where the number of individuals increases rapidly as resources become available.