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 as the base amount grows.

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 as the base amount shrinks.

Tags

CCSS.HSF-IF.C.8B

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How do you calculate the decay factor?

Back

The decay factor can be calculated as 1 minus the decay rate (in decimal form). For example, if the decay rate is 8%, the decay factor is 1 - 0.08 = 0.92.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for exponential growth?

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for exponential decay?

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

How do you determine the population after a certain number of years using exponential decay?

Back

To determine the population after a certain number of years, use the formula y = a(1 - r)^t, substituting 'a' for the initial population, 'r' for the decay rate, and 't' for the number of years.

Front

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

Back

The initial amount refers to the starting value of the quantity before any growth or decay occurs.

Tags

CCSS.HSF.LE.B.5

Front

What is the significance of the base in exponential functions?

Back

The base in exponential functions indicates the growth or decay factor. A base greater than 1 indicates growth, while a base less than 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B

Front

How can you classify a model as exponential growth or decay?

Back

A model can be classified as exponential growth if the growth factor (1 + r) is greater than 1, and as exponential decay if the decay factor (1 - r) is less than 1.

Tags

CCSS.HSF-IF.C.8B

Front

What is the effect of a higher growth rate on exponential growth?

Back

A higher growth rate results in a steeper increase in the quantity over time, leading to a larger final amount.

Tags

CCSS.HSF-IF.C.8B