Alg2 Statistics Review

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What is an exponential function?

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An exponential function is a mathematical function of the form y = a(b^x), where 'a' is a constant, 'b' is the base of the exponential (b > 0, b ≠ 1), and 'x' is the exponent. It describes growth or decay processes.

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What does the base of an exponential function indicate?

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The base of an exponential function indicates the growth (if b > 1) or decay (if 0 < b < 1) rate of the function.

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How do you find the exponential regression equation for a set of data?

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To find the exponential regression equation, use statistical software or a graphing calculator to fit an exponential model to the data points, typically in the form y = ab^x.

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What is the significance of the coefficient 'a' in an exponential function?

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The coefficient 'a' represents the initial value of the function when x = 0.

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What does it mean if an exponential function has a base less than 1?

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If the base is less than 1, the function represents exponential decay, meaning the value decreases over time.

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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 y = a(b^x), where 0 < b < 1.

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How can you determine if a polynomial is factorable?

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A polynomial is factorable if it can be expressed as a product of simpler polynomials. Techniques include factoring by grouping, using the quadratic formula, or synthetic division.

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What is the Factor Theorem?

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The Factor Theorem states that a polynomial f(x) has a factor (x - c) if and only if f(c) = 0.

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What is the difference between exponential growth and exponential decay?

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Exponential growth occurs when the base of the exponential function is greater than 1, leading to increasing values. Exponential decay occurs when the base is between 0 and 1, leading to decreasing values.

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What is the purpose of using regression analysis in statistics?

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Regression analysis is used to model the relationship between a dependent variable and one or more independent variables, allowing for predictions and insights into data trends.