Exponential Growth and Decay with Logs

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What is the definition of exponential growth?

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Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time. It can be represented by the function f(x) = a(1 + r)^x, where a is the initial amount and r is the growth rate.

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What is the definition of exponential decay?

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Exponential decay occurs when the decay rate of a value is proportional to its current value, leading to a decrease that slows over time. It can be represented by the function f(x) = a(1 - r)^x, where a is the initial amount and r is the decay rate.

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How do you identify exponential decay in a function?

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Exponential decay can be identified if the base of the exponent is between 0 and 1 (e.g., f(x) = a(0.20)^x).

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What is the relationship between logarithms and exponents?

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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 over equal intervals, while exponential growth increases by a percentage of the current value, leading to faster growth over time.

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What is the formula for exponential growth?

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The formula for exponential growth is f(t) = 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 the formula for exponential decay?

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The formula for exponential decay is f(t) = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

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