Exponential Growth and Decay

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What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Tags

CCSS.HSF-LE.A.1A

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What is exponential decay?

Back

Exponential decay is the process by which a quantity decreases at a rate proportional to its current value, resulting in a rapid decrease that slows over time.

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 compound interest?

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Compound interest can be calculated using the formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

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What is the significance of the base in exponential functions?

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In exponential functions, the base determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B

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What does a 30% annual decay rate mean in terms of a population?

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A 30% annual decay rate means that each year, the population will retain 70% of its previous year's population.

Tags

CCSS.HSF-IF.C.8B

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How do you interpret the value of 'x' in the equation y = a(0.7)^x?

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In the equation y = a(0.7)^x, 'x' represents the number of time periods (e.g., years) that have passed since the initial measurement.

Tags

CCSS.HSF.LE.B.5

Front

What is the impact of a 5% annual increase on an investment?

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A 5% annual increase means that the investment grows by 5% of its current value each year, leading to compound growth over time.

Tags

CCSS.HSF.BF.A.2

Front

How do you determine the future value of an investment using exponential growth?

Back

To determine the future value of an investment using exponential growth, apply the formula A = P(1 + r)^t, substituting the principal, growth rate, and time.

Tags

CCSS.HSF-IF.C.8B