Day 4: Exponential Functions Blitz

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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 determine?

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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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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.

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What is the initial value in an exponential function?

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The initial value in an exponential function is the value of the function when x = 0, represented as f(0) = a.

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How do you find the horizontal asymptote of an exponential function?

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The horizontal asymptote of an exponential function f(x) = a * b^x is typically y = 0, as x approaches negative infinity.

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What is the significance of the y-intercept in an exponential function?

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The y-intercept of an exponential function is the point where the graph crosses the y-axis, which occurs at (0, a). It represents the initial value of the function.

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How can you identify exponential growth from a graph?

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Exponential growth can be identified from a graph by a curve that rises steeply as x increases, indicating that the function's value increases rapidly.

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What is the formula for exponential decay?

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The formula for exponential decay is f(x) = a * b^x, where 0 < b < 1.

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What does it mean for a function to have a horizontal asymptote?

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A horizontal asymptote indicates the value that a function approaches as x approaches positive or negative infinity, but never actually reaches.

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How do you determine the growth factor in an exponential function?

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The growth factor in an exponential function is the base 'b' in the equation f(x) = a * b^x, which indicates how much the function multiplies by for each unit increase in x.