Exponential Growth & Decay

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What is Exponential Growth?

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Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate. Example: A population of bacteria doubles every hour.

Tags

CCSS.HSF-LE.A.1A

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What is Exponential Decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, leading to a rapid decline. Example: A radioactive substance decays by 5% each year.

Tags

CCSS.HSF-IF.C.8B

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Define the Common Ratio in exponential functions.

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The common ratio is the factor by which a quantity multiplies during each time period in exponential growth or decay. Example: In the function y = a(r)^x, r is the common ratio.

Tags

CCSS.HSF-IF.C.8B

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What is the formula for Exponential Growth?

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

Tags

CCSS.HSF-IF.C.8B

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What is the formula for Exponential Decay?

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

Tags

CCSS.HSF-IF.C.8B

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How do you calculate the population after a certain number of years with exponential decay?

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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.

Tags

CCSS.HSF-LE.A.1A

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What does a Common Ratio of 1 indicate?

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A common ratio of 1 indicates that the quantity remains constant over time, showing no growth or decay.

Tags

CCSS.HSF.BF.A.2

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If a quantity decreases by 30% each year, what is the common ratio?

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The common ratio is 0.7, calculated as 1 - 0.30.

Tags

CCSS.HSF.BF.A.2

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Write the equation for a population that starts at 8000 and decreases by 6% per year.

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y = 8000(0.94)^t.

Tags

CCSS.HSF.LE.A.2

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What is the significance of the base in an exponential function?

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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