ET_ Exponential Functions From Tables

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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 of the exponential (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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How can you identify an exponential function from a table of values?

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An exponential function can be identified from a table of values if the ratio of consecutive outputs (y-values) is constant when the inputs (x-values) are increased by the same amount.

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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 0 < b < 1.

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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 b > 1.

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How do you write an exponential function from a given table of values?

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To write an exponential function from a table, identify the initial value (y-intercept) and the base by determining the constant ratio of the outputs for equal increments in the inputs.

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What is the significance of the initial value in an exponential function?

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The initial value in an exponential function represents the output when x = 0, which is the y-intercept of the graph.

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What does the term 'exponential growth' mean?

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Exponential growth refers to an increase in quantity where the rate of growth is proportional to the current value, leading to rapid increases over time.

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What does the term 'exponential decay' mean?

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Exponential decay refers to a decrease in quantity where the rate of decay is proportional to the current value, leading to rapid decreases over time.

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How can you convert an exponential function from one form to another?

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You can convert an exponential function from one form to another by factoring out constants or changing the base using logarithmic properties.