Exponential Growth and 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 as the base amount grows.

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What is exponential decay?

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Exponential decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to a rapid decrease as the base amount shrinks.

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How do you calculate the decay factor?

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The decay factor can be calculated as 1 minus the decay rate (in decimal form). For example, if the decay rate is 8%, the decay factor is 1 - 0.08 = 0.92.

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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.

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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.

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How do you determine the population after a certain number of years using exponential decay?

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To determine the population after a certain number of years, use the formula y = a(1 - r)^t, substituting 'a' for the initial population, 'r' for the decay rate, and 't' for the number of years.

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What does the term 'initial amount' refer to in exponential functions?

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The initial amount refers to the starting value of the quantity before any growth or decay occurs.

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What is the significance of the base in exponential functions?

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The base in exponential functions indicates the growth or decay factor. A base greater than 1 indicates growth, while a base less than 1 indicates decay.

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How can you classify a model as exponential growth or decay?

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A model can be classified as exponential growth if the growth factor (1 + r) is greater than 1, and as exponential decay if the decay factor (1 - r) is less than 1.

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What is the effect of a higher growth rate on exponential growth?

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A higher growth rate results in a steeper increase in the quantity over time, leading to a larger final amount.