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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What is the common ratio in an exponential function?

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The common ratio (or multiplier) in an exponential function is the base 'b' raised to the power of 'x'. It determines how much the function grows or decays.

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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 'a', which represents the initial value when x = 0.

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How do you identify 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.

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How do you identify 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.

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What is the general form of an exponential growth function?

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The general form of an exponential growth function is f(x) = a(b)^x, where b > 1.

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

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What does the term 'initial value' refer to in an exponential function?

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The initial value refers to the y-intercept of the function, which is the value of the function when x = 0.

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What is the effect of changing the base 'b' in an exponential function?

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Changing the base 'b' affects the rate of growth or decay; a larger base results in faster growth, while a smaller base (greater than 0) results in slower growth or decay.

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How can you determine if a function is linear or exponential?

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A function is linear if it can be expressed in the form f(x) = mx + b, where m and b are constants. It is exponential if it can be expressed in the form f(x) = a(b)^x.