Writing Exponential Equations

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What is an exponential equation?

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An exponential equation is an equation in which a variable appears in the exponent. For example, y = a * b^x, where a and b are constants.

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What is the general form of an exponential function?

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The general form of an exponential function is f(x) = a * b^x, where a is a constant, b is the base (b > 0, b ≠ 1), and x is the exponent.

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How do you identify the base in an exponential equation?

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The base in an exponential equation is the constant that is raised to the power of the variable. For example, in y = 3 * 2^x, the base is 2.

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What does it mean for an exponential function to be increasing?

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An exponential function is increasing if the base (b) is greater than 1. This means that as x increases, f(x) also increases.

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What does it mean for an exponential function to be decreasing?

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An exponential function is decreasing if the base (b) is between 0 and 1. This means that as x increases, f(x) decreases.

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What is the y-intercept of an exponential function?

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The y-intercept of an exponential function f(x) = a * b^x is the value of f(0), which equals a.

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How do you solve an exponential equation?

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To solve an exponential equation, you can take the logarithm of both sides or rewrite the equation in a form that allows you to isolate the variable.

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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, while exponential decay occurs when the base is between 0 and 1.

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What is a real-world example of exponential growth?

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A real-world example of exponential growth is population growth, where the population increases at a rate proportional to its current size.

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What is a real-world example of exponential decay?

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A real-world example of exponential decay is radioactive decay, where the quantity of a radioactive substance decreases over time.