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 of the exponential (b > 0, b ≠ 1), and x is the exponent.

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What is the general form of an exponential equation?

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The general form of an exponential equation is y = a * b^(cx + d), where a, b, c, and d are constants.

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How do you solve an exponential equation?

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To solve an exponential equation, isolate the exponential expression, take the logarithm of both sides, and then solve for the variable.

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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 rate of growth or decay.

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What is the natural exponential function?

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The natural exponential function is an exponential function with base e (approximately 2.718), denoted as f(x) = e^x.

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What is the value of e (Euler's number)?

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Euler's number e is approximately equal to 2.71828 and is the base of the natural logarithm.

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What is the relationship between exponential functions and logarithms?

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Exponential functions and logarithms are inverse operations; if y = b^x, then x = log_b(y).

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How do you convert an exponential equation to logarithmic form?

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To convert an exponential equation a^b = c to logarithmic form, write it as log_a(c) = b.

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What is the exponential growth formula?

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The exponential growth formula is P(t) = P_0 * e^(rt), where P_0 is the initial amount, r is the growth rate, and t is time.

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What is the exponential decay formula?

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The exponential decay formula is P(t) = P_0 * e^(-rt), where P_0 is the initial amount, r is the decay rate, and t is time.