Alg 1 Unit 4 Review

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What is Exponential Decay?

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Exponential Decay refers to a process where a quantity decreases at a rate proportional to its current value, often represented by the function f(x) = a(1 - r)^t, where 0 < r < 1.

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How can you identify Exponential Decay in a function?

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You can identify Exponential Decay in a function by checking if the base of the exponent is less than one. For example, in f(x) = 25(0.20)^x, the base 0.20 indicates decay.

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What is the general form of an Exponential Growth function?

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The general form of an Exponential Growth function 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 does the term 'base' refer to in exponential functions?

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In exponential functions, the 'base' is the constant that is raised to a power. It determines the rate of growth or decay.

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What is the significance of a negative exponent?

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What is the formula for calculating compound interest?

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The formula for calculating compound interest is A = P(1 + r/n)^{nt}, where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

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This equation represents exponential growth in real-world scenarios, such as population growth, investment growth, or any situation where a quantity increases over time.

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What is the difference between exponential growth and exponential decay?

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Exponential growth occurs when a quantity increases over time, while exponential decay occurs when a quantity decreases over time.