Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth that accelerates over time.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, resulting in a rapid decrease that slows over time.

Tags

CCSS.HSF-IF.C.8B

Front

Provide an example of a sequence that represents exponential growth.

Back

An example of exponential growth is the sequence 2, 4, 8, 16, 32, ... where each term is multiplied by 2.

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CCSS.HSF.BF.A.2

Front

Provide an example of a sequence that represents exponential decay.

Back

An example of exponential decay is the sequence 100, 50, 25, 12.5, ... where each term is halved.

Tags

CCSS.HSF.BF.A.2

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What is the general formula for exponential growth?

Back

The general formula for exponential growth is f(t) = a * e^(kt), where 'a' is the initial amount, 'k' is the growth rate, and 't' is time.

Tags

CCSS.HSF-LE.A.1A

Front

What is the general formula for exponential decay?

Back

The general formula for exponential decay is f(t) = a * e^(-kt), where 'a' is the initial amount, 'k' is the decay rate, and 't' is time.

Tags

CCSS.HSF-LE.A.1A

Front

How do you identify exponential growth on a graph?

Back

Exponential growth on a graph is identified by a curve that rises steeply and continuously increases as it moves to the right.

Tags

CCSS.HSF-IF.C.7E

Front

How do you identify exponential decay on a graph?

Back

Exponential decay on a graph is identified by a curve that falls steeply and continuously decreases as it moves to the right.

Tags

CCSS.HSF-IF.C.7E

Front

What does the base of an exponential function indicate?

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The base of an exponential function indicates the growth or decay factor; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is the significance of the y-intercept in an exponential function?

Back

The y-intercept of an exponential function represents the initial value of the quantity before any growth or decay occurs.

Tags

CCSS.HSF-IF.C.7E