Exponential Word Problems

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What is an exponential decay function?

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An exponential decay function describes a situation where a quantity decreases at a rate proportional to its current value, often represented as y = a * e^(-kt), where 'a' is the initial amount, 'k' is the decay constant, and 't' is time.

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What is an exponential growth function?

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An exponential growth function describes a situation where a quantity increases at a rate proportional to its current value, often represented as y = a * e^(kt), where 'a' 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 exponential growth?

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To calculate the future value of an investment with exponential growth, use the formula: Future Value = Present Value * (1 + r)^t, where 'r' is the growth rate and 't' is the number of time periods.

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How do you calculate the future value of an asset with exponential decay?

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To calculate the future value of an asset with exponential decay, use the formula: Future Value = Present Value * (1 - r)^t, where 'r' is the decay rate and 't' is the number of time periods.

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What is the significance of the decay rate in exponential decay problems?

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The decay rate indicates how quickly the quantity decreases over time. A higher decay rate results in a faster decrease in value.

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What is the significance of the growth rate in exponential growth problems?

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The growth rate indicates how quickly the quantity increases over time. A higher growth rate results in a faster increase in value.

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What is the doubling time in exponential growth?

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Doubling time is the period it takes for a quantity to double in size, often calculated using the rule of 70: Doubling Time (in years) = 70 / growth rate (as a percentage).

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What is the half-life in exponential decay?

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Half-life is the time required for a quantity to reduce to half its initial value, commonly used in contexts like radioactive decay.

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How do you interpret the results of exponential growth and decay in real-world scenarios?

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Exponential growth and decay can model various real-world phenomena, such as population growth, financial investments, and depreciation of assets.

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What is the formula for continuous compounding in finance?

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The formula for continuous compounding is A = Pe^(rt), where 'A' is the amount of money accumulated after time 't', 'P' is the principal amount, 'r' is the annual interest rate, and 'e' is Euler's number.