BR 11/5/24 Exponential Functions

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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 the base of an exponential function represent?

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

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How do you find the value of an exponential function at a specific point?

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To find the value of an exponential function at a specific point, substitute the value of 'x' into the function and calculate the result.

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What is the y-intercept of an exponential function?

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The y-intercept of an exponential function is the point where the graph intersects the y-axis, which occurs when x=0. It can be found by evaluating the function at x=0.

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What is exponential growth?

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Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to an increase that accelerates over time.

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What is exponential decay?

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Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to a decrease that slows over time.

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What is an asymptote in the context of exponential functions?

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An asymptote is a line that a graph approaches but never touches. In exponential functions, horizontal asymptotes often represent a value that the function approaches as x approaches infinity.

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How do you determine the horizontal asymptote of an exponential decay function?

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The horizontal asymptote of an exponential decay function is typically the value that the function approaches as x approaches infinity, often represented as y = k, where k is a constant.

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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 f(x) = a * b^x, where 'a' is the initial value and 'b' is the growth factor (b > 1).

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What is the general form of an exponential decay function?

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