Algebra 2, Unit 4: Exponential and Logarithmic Functions. Key terms, formulas, and worked-example cues a high school student meets for this unit, building on prior units. Front: the term, formula name, or short problem cue. Back: the definition, formula, or solution method.
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- What is an exponential function?
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A function of the form f(x) = a times b^x, where b is a positive constant- What does the base 'b' in an exponential function represent?
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The growth or decay factor- What does it mean if the base of an exponential function is greater than 1?
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The function represents exponential growth- What does it mean if the base of an exponential function is between 0 and 1?
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The function represents exponential decay- What is the general form of an exponential growth model?
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y = a(1 + r)^t- What is the general form of an exponential decay model?
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y = a(1 - r)^t- What is the natural base e approximately equal to?
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2.718- What is a logarithm?
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The exponent to which a base must be raised to produce a given number- What is the logarithmic form of b^x = y?
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log_b(y) = x- What is a common logarithm?
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A logarithm with base 10- What is a natural logarithm?
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A logarithm with base e, written ln(x)- What is the inverse function of an exponential function?
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A logarithmic function with the same base- What is the product rule of logarithms?
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log_b(MN) = log_b(M) + log_b(N)- What is the quotient rule of logarithms?
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log_b(M/N) = log_b(M) - log_b(N)- What is the power rule of logarithms?
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log_b(M^p) = p times log_b(M)
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