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. It can be represented by the formula y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

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What is exponential decay?

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Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline. It can be represented by the formula y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

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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 'y' is the final amount, 'a' is the initial amount, 'r' is the growth rate (as a decimal), and 't' is the time period.

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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 'y' is the final amount, 'a' is the initial amount, 'r' is the decay rate (as a decimal), and 't' is the time period.

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How do you calculate the value of an investment after a certain number of years with exponential growth?

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To calculate the value of an investment after a certain number of years with exponential growth, use the formula y = a(1 + r)^t, substituting 'a' with the initial investment, 'r' with the annual growth rate, and 't' with the number of years.

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How do you calculate the value of an investment after a certain number of years with exponential decay?

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To calculate the value of an investment after a certain number of years with exponential decay, use the formula y = a(1 - r)^t, substituting 'a' with the initial investment, 'r' with the annual decay rate, and 't' with the number of years.

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What does a decay rate of 10% mean in terms of exponential decay?

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A decay rate of 10% means that each year, the quantity decreases to 90% of its value from the previous year. This can be represented by the formula y = a(0.90)^t.

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If a population is 3,370,000 and decreases at a rate of 10%, what is the equation representing this situation?

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The equation representing this situation is y = (0.90^t)(3,370,000).

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If a home is worth $160,000 and increases in value by 5% per year, what is its value after 2 years?

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The value of the home after 2 years is $176,400, calculated using the formula y = 160,000(1.05)^2.

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What is the initial amount in the function y = 15(1.35)^t?

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The initial amount in the function y = 15(1.35)^t is $15.