Exponential Growth and Decay

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What is exponential growth?

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Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase that can be modeled by the equation y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

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 a period of time, resulting in a rapid decrease that can be modeled by the equation 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 express a quantity that doubles every week?

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A quantity that doubles every week can be expressed as y = a(2)^t, where a is the initial amount and t is the number of weeks.

Tags

CCSS.HSF.LE.A.2

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What is the formula for calculating the remaining amount after a percentage decay?

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The formula for calculating the remaining amount after a percentage 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 classify a model as exponential growth or decay?

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A model is classified as exponential growth if the base of the exponent is greater than 1 (e.g., y = a(1 + r)^t), and as exponential decay if the base is between 0 and 1 (e.g., y = a(1 - r)^t).

Tags

CCSS.HSF-IF.C.8B

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What does the variable 'x' represent in exponential equations?

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In exponential equations, 'x' typically represents time, often measured in years, weeks, or other time intervals.

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What is the significance of the initial amount 'a' in exponential models?

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

Tags

CCSS.HSF.LE.B.5

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How do you calculate the growth factor from a percentage growth rate?

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To calculate the growth factor from a percentage growth rate, convert the percentage to a decimal and add 1. For example, a 14% growth rate has a growth factor of 1 + 0.14 = 1.14.

Tags

CCSS.HSF-IF.C.8B

Front

How do you calculate the decay factor from a percentage decay rate?

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To calculate the decay factor from a percentage decay rate, convert the percentage to a decimal and subtract it from 1. For example, a 30% decay rate has a decay factor of 1 - 0.30 = 0.70.

Tags

CCSS.HSF-IF.C.8B

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What is the general form of an exponential growth equation?

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The general form of an exponential growth equation 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