Exponential Function Flashcard

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What is an exponential function?

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An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

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What does it mean for a function to exhibit exponential decay?

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Exponential decay occurs when a quantity decreases at a rate proportional to its current value, typically represented by a function of the form f(x) = a * (1 - r)^x, where 'r' is the decay rate.

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How do you identify an exponential function from an equation?

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An exponential function can be identified by the variable being in the exponent, such as in the form f(x) = a * b^x.

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What is the general form of an exponential decay equation?

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The general form of an exponential decay equation is y = a * (1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.

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What is the horizontal asymptote of an exponential decay function?

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The horizontal asymptote of an exponential decay function is y = 0, meaning the function approaches but never reaches zero.

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What is the initial value in an exponential decay problem?

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The initial value is the starting amount before any decay occurs, often represented by 'a' in the equation y = a * (1 - r)^x.

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How do you calculate the decay factor from a percentage?

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The decay factor can be calculated by subtracting the decay percentage from 1. For example, if the decay rate is 30%, the decay factor is 1 - 0.30 = 0.70.

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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 at a rate proportional to its current value, while exponential decay occurs when a quantity decreases at a rate proportional to its current value.

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What does the base of an exponential function represent?

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The base of an exponential function represents the growth or decay factor. If the base is greater than 1, it indicates growth; if it is between 0 and 1, it indicates decay.

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How can you determine if a function is linear or exponential?

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A function is linear if it can be expressed in the form y = mx + b, where 'm' is the slope. It is exponential if the variable is in the exponent, such as y = a * b^x.