Exponential Growth and Decay

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What is the formula for exponential growth?

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The formula for exponential growth is given by: y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate (as a decimal), and 'x' is the time in years.

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What is the formula for exponential decay?

Back

The formula for exponential decay is given by: y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate (as a decimal), and 'x' is the time in years.

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How do you find the decay factor from a percentage?

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The decay factor can be found by subtracting the decay rate from 1. For example, if the decay rate is 6%, the decay factor is 1 - 0.06 = 0.94.

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What is the initial value in an exponential function?

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The initial value in an exponential function is the value of 'y' when 'x' is 0, represented by 'a' in the formula y = a(1 + r)^x.

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If a population decreases by 20% each year, what is the decay factor?

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The decay factor is 1 - 0.20 = 0.80.

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How do you calculate the value after a certain number of years in exponential growth?

Back

To calculate the value after 'x' years in exponential growth, use the formula: y = a(1 + r)^x.

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How do you calculate the value after a certain number of years in exponential decay?

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To calculate the value after 'x' years in exponential decay, use the formula: y = a(1 - r)^x.

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What is the value of a painting worth $1400 after 3 years with a 9% increase?

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Using the formula y = 1400(1.09)^3, the value after 3 years is approximately $1835.64.

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What is the value of an investment of $600 after 5 years at a 5% interest rate?

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Using the formula y = 600(1 + 0.05)^5, the value after 5 years is approximately $765.77.

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What does the term 'growth rate' mean in exponential functions?

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The growth rate is the percentage increase in value over a specific period, expressed as a decimal in the exponential growth formula.