Exponential Growth and Decay

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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 the time period.

Tags

CCSS.HSF-IF.C.8B

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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 period.

Tags

CCSS.HSF-IF.C.8B

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How do you convert a percentage growth rate to a decimal for calculations?

Back

To convert a percentage growth rate to a decimal, divide the percentage by 100. For example, 35% becomes 0.35.

Tags

CCSS.HSF-IF.C.8B

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What does it mean for a population to decrease by a certain percentage each year?

Back

It means that each year, the population is reduced by that percentage of its current size.

Tags

CCSS.HSF-LE.A.1C

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How do you calculate the value of an asset after depreciation?

Back

To calculate the value of an asset after depreciation, use the formula: Value = Initial Cost × (1 - Depreciation Rate)^t.

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What is the significance of the initial amount in exponential functions?

Back

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

Tags

CCSS.HSF.LE.B.5

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How can you determine the population after a certain number of years with a given growth rate?

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Use the exponential growth formula: y = a(1 + r)^t, substituting 'a' with the initial population, 'r' with the growth rate, and 't' with the number of years.

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What is the difference between linear growth and exponential growth?

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

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How do you find the total population after multiple periods of growth?

Back

You can use the exponential growth formula repeatedly for each period or calculate it directly using the formula for the total period.

Tags

CCSS.HSF-LE.A.1C

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What is the impact of a higher growth rate on the final amount in exponential growth?

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A higher growth rate results in a significantly larger final amount due to the compounding effect of growth.

Tags

CCSS.HSF-IF.C.8B