Exponential Growth and Decay

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What is exponential growth?

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Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate over time.

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CCSS.HSF-LE.A.1A

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What is exponential decay?

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Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

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CCSS.HSF-IF.C.8B

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What is linear decay?

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Linear decay refers to a constant decrease in a quantity over time, represented by a straight line on a graph.

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CCSS.HSF-IF.C.7A

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How can you identify exponential growth on a graph?

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Exponential growth is identified by a smooth curve that rises steeply as time progresses.

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CCSS.HSF-IF.C.7E

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How can you identify exponential decay on a graph?

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Exponential decay is identified by a smooth curve that decreases rapidly at first and then levels off.

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CCSS.HSF-IF.C.7E

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What is the general formula for exponential growth?

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The general formula for exponential growth is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

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CCSS.HSF-IF.C.8B

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What is the general formula for exponential decay?

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The general formula for exponential decay is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

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CCSS.HSF-IF.C.8B

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What is the difference between exponential and linear functions?

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Exponential functions grow or decay at rates proportional to their current value, while linear functions change at a constant rate.

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What are some real-world examples of exponential growth?

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Examples include population growth, compound interest, and the spread of diseases.

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What are some real-world examples of exponential decay?

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Examples include radioactive decay, depreciation of assets, and cooling of hot objects.