Exponential Growth and Decay

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What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a constant percentage over a period of time. The general formula is: 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?

Back

Exponential Decay occurs when a quantity decreases by a constant percentage over a period of time. The general formula is: 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 decay factor in exponential decay?

Back

The decay factor is calculated as (1 - r), where 'r' is the decay rate expressed as a decimal.

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How do you write an exponential decay equation for a quantity that decreases by 30% each year starting from 5000?

Back

The equation is y = 5000(0.7)^x, where x is the number of years.

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If a car's value is $15,000 and it depreciates at 8% per year, what is the decay factor?

Back

The decay factor is 0.92, calculated as (1 - 0.08).

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How do you calculate the future value of an investment with a 5% annual growth rate over 20 years starting from $160,000?

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Use the formula: Future Value = 160000(1 + 0.05)^20, which equals approximately $424,527.63.

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What does the equation f(x) = 25(0.20)^x represent?

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This represents Exponential Decay, as the base (0.20) is less than 1.

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What is the growth factor in the equation f(x) = 0.75(0.96)^3?

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The growth factor is 0.96, indicating a decay since it is less than 1.

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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, while exponential growth increases by a constant percentage, leading to faster growth over time.

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What is the formula for calculating the value of an investment after 't' years with a growth rate 'r'?

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The formula is: Future Value = Initial Amount * (1 + r)^t.