Exponential Growth & Decay

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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. For example, if a population grows by 10% each year, it grows faster as the population increases.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

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. For example, radioactive substances decay exponentially.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential growth equation?

Back

Front

What is the general form of an exponential decay equation?

Back

Tags

CCSS.HSF-IF.C.8B

Front

How do you find the growth rate from an exponential growth equation?

Back

Tags

CCSS.HSF-IF.C.8B

Front

How do you find the decay rate from an exponential decay equation?

Back

Tags

CCSS.HSF-IF.C.8B

Front

What does the base of an exponential function represent?

Back

In an exponential function, the base 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 initial value 'a' in an exponential equation?

Back

The initial value 'a' represents the starting amount before any growth or decay occurs.

Tags

CCSS.HSF.LE.B.5

Front

If a population doubles every 5 years, what is the growth factor?

Back

The growth factor is 2, indicating that the population multiplies by 2 every 5 years.

Tags

CCSS.HSF-LE.A.1A

Front

What is the relationship between growth rate and decay rate?

Back

The growth rate is the percentage increase, while the decay rate is the percentage decrease. They are complementary; for example, a 10% growth rate corresponds to a 10% decay rate in the context of the remaining quantity.

Tags

CCSS.HSF-IF.C.8B