Exponential Growth and Decay

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What is exponential growth?

Back

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 10% each year, it will grow faster each subsequent year.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to a rapid decrease. For example, if a substance loses 20% of its mass every hour, it will decay faster each hour.

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CCSS.HSF-IF.C.8B

Front

Write the general formula for exponential growth.

Back

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CCSS.HSF-IF.C.8B

Front

Write the general formula for exponential decay.

Back

Tags

CCSS.HSF-IF.C.8B

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Back

In the exponential function, the base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor. It indicates how much the quantity changes for each unit increase in x.

Tags

CCSS.HSF-IF.C.8B

Front

If a population of bacteria doubles every hour, what type of growth is this?

Back

This is an example of exponential growth.

Tags

CCSS.HSF-LE.A.1A

Front

If a car's value decreases by 15% each year, what type of function models this situation?

Back

This situation is modeled by an exponential decay function.

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What is the horizontal asymptote of an exponential decay function?

Back

The horizontal asymptote of an exponential decay function is y = 0, meaning the value approaches zero but never actually reaches it.

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CCSS.HSF-IF.C.7E

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Back

The value 24000 represents the initial value of the car when t = 0.

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CCSS.HSF.LE.B.5

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What does it mean if a function is described as having exponential decay?

Back

It means that the function's output decreases over time, typically represented by a base less than 1 in the exponential function.

Tags

CCSS.HSF-IF.C.8B