Exponential Growth & Decay

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What is Exponential Growth?

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Exponential Growth occurs when a quantity increases by a fixed percentage over a period of time, resulting in a rapid increase. For example, if a population grows by 20% each year, it will grow faster each subsequent year.

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What is Exponential Decay?

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Exponential Decay is the process where a quantity decreases by a fixed percentage over time. For example, if a substance decays at a rate of 10% per year, it will lose 10% of its remaining amount each year.

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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 (as a decimal), and 't' is the time period.

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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 (as a decimal), and 't' is the time period.

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How do you calculate the future value in Exponential Growth?

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To calculate the future value in Exponential Growth, use the formula: Future Value = Initial Amount * (1 + Growth Rate)^Number of Periods.

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How do you calculate the future value in Exponential Decay?

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To calculate the future value in Exponential Decay, use the formula: Future Value = Initial Amount * (1 - Decay Rate)^Number of Periods.

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If a population of 100 increases by 50% each year, how many will there be after 2 years?

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After 2 years, the population will be 100 * (1 + 0.5)^2 = 225.

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If a substance has an initial amount of 200 and decays by 20% each year, how much will remain after 3 years?

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After 3 years, the remaining amount will be 200 * (1 - 0.2)^3 = 128.

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What is the difference between linear growth and exponential growth?

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

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What does a graph of Exponential Growth look like?

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A graph of Exponential Growth shows a curve that rises steeply, indicating rapid increases as time progresses.