Solving 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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How do you solve an exponential equation?

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To solve an exponential equation, you typically rewrite both sides of the equation with the same base, then set the exponents equal to each other.

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What is the base of an exponential function?

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The base of an exponential function is the constant 'b' in the function f(x) = a * b^x, which determines the growth or decay rate.

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What does it mean for a function to exhibit exponential growth?

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Exponential growth occurs when the base 'b' in the function f(x) = a * b^x is greater than 1, resulting in the function increasing rapidly as 'x' increases.

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What does it mean for a function to exhibit exponential decay?

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Exponential decay occurs when the base 'b' in the function f(x) = a * b^x is between 0 and 1, resulting in the function decreasing rapidly as 'x' increases.

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How can you express 8 as a power of 2?

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8 can be expressed as 2^3, since 2 * 2 * 2 = 8.

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What is the first step in solving the equation 8 = 2^(5x + 7)?

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The first step is to rewrite 8 as 2^3, allowing you to set the exponents equal: 3 = 5x + 7.

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What is the relationship between the bases when solving exponential equations?

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When solving exponential equations, the bases must be the same in order to equate the exponents.

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How do you rewrite 36 as a power of 6?

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36 can be rewritten as 6^2, since 6 * 6 = 36.

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What is the general form of an exponential decay equation?

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The general form of an exponential decay equation is y = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.