Exponential Growth and Decay

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What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a consistent 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

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What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a consistent percentage over time. For example, if a substance loses 20% of its mass each year, it will decrease rapidly in the initial years.

Tags

CCSS.HSF-IF.C.8B

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How do you convert a percentage to a decimal?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 11.2% becomes 0.112.

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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 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 time.

Tags

CCSS.HSF-IF.C.8B

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What does the base of an exponential function represent?

Back

The base of an exponential function represents the growth or decay factor. For example, in f(x) = a(b)^x, 'b' indicates how much the quantity increases (if b > 1) or decreases (if 0 < b < 1).

Tags

CCSS.HSF-IF.C.8B

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If a population of bacteria doubles every 3 hours, what type of growth is this?

Back

This is an example of Exponential Growth, as the population increases rapidly over time.

Tags

CCSS.HSF-LE.A.1A

Front

What is the growth rate in the function f(x)=2(1.44)^x?

Back

The growth rate is 44%, as the base (1.44) indicates a 44% increase.

Tags

CCSS.HSF-IF.C.8B

Front

How do you identify Exponential Growth vs. Exponential Decay?

Back

Exponential Growth has a base greater than 1 (e.g., 1.01), while Exponential Decay has a base between 0 and 1 (e.g., 0.7).

Tags

CCSS.HSF-IF.C.8B

Front

Write the equation for a culture of bacteria that starts with 5000 cells and dies by 30% each year.

Back

The equation is y = 5000(0.7)^x, where 0.7 represents the 70% of cells remaining after a 30% decay.

Tags

CCSS.HSF.LE.A.2