Exponential Growth and Decay

Front

What is exponential growth?

Back

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

Tags

CCSS.HSF-LE.A.1A

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What is exponential decay?

Back

Exponential decay describes a decrease in quantity where the rate of decrease is proportional to the current amount, resulting in a rapid decline.

Tags

CCSS.HSF-IF.C.8B

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How can you identify an exponential function?

Back

Front

What does the base of an exponential function indicate?

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The base indicates the growth or decay factor. If the base is greater than 1, it represents growth; if between 0 and 1, it represents decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential growth equation?

Back

Tags

CCSS.HSF-LE.A.1A

Front

What is the general form of an exponential decay equation?

Back

Tags

CCSS.HSF-IF.C.8B

Front

Back

0.85 represents the decay factor, indicating that the quantity decreases to 85% of its previous value each time period.

Tags

CCSS.HSF.LE.B.5

Front

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

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The initial value is the starting amount before any growth or decay occurs, often represented by 'A_0'.

Front

How do you determine if a function is exponential from a table of values?

Back

If the ratio of consecutive values remains constant, the function is exponential.

Tags

CCSS.HSF-LE.A.1A

Front

What is the difference between linear and exponential growth?

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Linear growth increases by a constant amount, while exponential growth increases by a percentage of the current value, leading to faster growth over time.