Exponential Growth and Decay

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What is exponential growth?

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Exponential growth occurs when the increase in a quantity is proportional to its current value, leading to growth at an increasing rate. For example, if a population of bacteria doubles every hour, it exhibits exponential growth.

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What is exponential decay?

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Exponential decay refers to the process where a quantity decreases at a rate proportional to its current value, leading to a rapid decrease initially that slows over time. An example is radioactive decay.

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What does the base of an exponential function represent in growth scenarios?

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In growth scenarios, the base of an exponential function represents the growth factor. For example, a base of 1.12 indicates a growth rate of 12%.

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What does the base of an exponential function represent in decay scenarios?

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In decay scenarios, the base of an exponential function represents the decay factor. For example, a base of 0.97 indicates a decay rate of 3%.

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How do you interpret the initial value in an exponential function?

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What is the formula for exponential growth?

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What is the formula for exponential decay?

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How do you find the number of cells after a certain time if they double every hour?

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What is the significance of the exponent in an exponential function?

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The exponent in an exponential function indicates the number of time intervals that have passed, affecting the total amount through repeated multiplication by the growth or decay factor.

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How can you determine the remaining quantity after a certain number of periods in a decay scenario?

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