Exponential Growth and Decay Word Problems

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What is exponential decay?

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Exponential decay refers to a decrease in a quantity at a rate proportional to its current value, often represented by the formula A = A0 * e^(-kt), where A0 is the initial amount, k is the decay constant, and t is time.

Front

What is exponential growth?

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Exponential growth occurs when a quantity increases at a rate proportional to its current value, typically modeled by the formula A = A0 * e^(kt), where A0 is the initial amount, k is the growth constant, and t is time.

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How do you calculate the future value of an investment with compound interest?

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The future value (FV) can be calculated using the formula FV = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

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What is the formula for calculating depreciation?

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The formula for calculating depreciation is V = P(1 - r)^t, where V is the value after t years, P is the initial value, r is the depreciation rate, and t is the time in years.

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What does it mean for a quantity to decrease by a percentage each year?

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It means that each year, the quantity is reduced by that percentage of its current value, leading to a smaller amount each subsequent year.

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If a quantity decreases by 10% each year, what is the remaining percentage after 3 years?

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The remaining percentage after 3 years is (0.9)^3 = 0.729 or 72.9% of the original quantity.

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What is the significance of rounding in exponential problems?

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Rounding is important in exponential problems to provide a practical and usable answer, especially in financial contexts where cents matter.

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How do you interpret a 5% annual reduction in emissions?

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A 5% annual reduction means that each year, the emissions will be 95% of the previous year's emissions, leading to a gradual decrease over time.

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What is the impact of compounding frequency on interest earned?

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The more frequently interest is compounded, the more interest will be earned, as interest is calculated on previously earned interest.

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How do you find the value of a depreciating asset after a certain number of years?

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Use the depreciation formula V = P(1 - r)^t, substituting the initial value, depreciation rate, and number of years.