Exponential Growth and Decay

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What is Exponential Growth?

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Exponential Growth occurs when a quantity increases by a constant percentage over a period of time. For example, if a population grows by 10% each year, it is experiencing exponential growth.

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What is Exponential Decay?

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Exponential Decay occurs when a quantity decreases by a constant percentage over a period of time. For example, if a substance loses 20% of its mass every hour, it is experiencing exponential decay.

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What is the general form of an exponential function?

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The general form of an exponential function is f(x) = a(b)^x, where 'a' is the initial value, 'b' is the base (growth factor if b > 1, decay factor if 0 < b < 1), and 'x' is the exponent.

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What does the base 'b' represent in an exponential function?

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In an exponential function f(x) = a(b)^x, the base 'b' represents the growth or decay factor. If b > 1, it indicates growth; if 0 < b < 1, it indicates decay.

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How do you identify exponential growth from a function?

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Exponential growth can be identified if the base 'b' in the function f(x) = a(b)^x is greater than 1.

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How do you identify exponential decay from a function?

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Exponential decay can be identified if the base 'b' in the function f(x) = a(b)^x is between 0 and 1.

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What is the common ratio in exponential functions?

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The common ratio in exponential functions is the factor by which the quantity changes for each unit increase in x. It is represented by 'b' in the function f(x) = a(b)^x.

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What is the range of an exponential function?

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The range of an exponential function f(x) = a(b)^x is (0, ∞) if a > 0, meaning it can take any positive value.

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What is the domain of an exponential function?

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The domain of an exponential function f(x) = a(b)^x is all real numbers, represented as (-∞, ∞).

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What is the effect of a negative exponent in an exponential function?

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A negative exponent in an exponential function indicates decay. For example, f(x) = a(b)^(-x) represents exponential decay.