Exponential Functions Review

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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. It shows rapid growth or decay.

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What does the y-intercept represent in an exponential function?

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The y-intercept is the value of the function when x = 0. It represents the initial amount or starting value of the function.

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How do you identify the initial value in the function f(x) = 13(0.27)^x?

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The initial value is the coefficient 'a' in the function, which is 13 in this case.

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What is the formula for exponential growth?

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The formula for exponential growth is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

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What is the formula for exponential decay?

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The formula for exponential decay is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

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How do you convert a percentage increase to a growth factor?

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To convert a percentage increase to a growth factor, use the formula: Growth Factor = 1 + (percentage increase / 100). For example, a 35% increase becomes 1 + 0.35 = 1.35.

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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 the initial value and 'b' is the base.

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How do you find the multiplier in an exponential function?

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The multiplier is the base 'b' in the function f(x) = a * b^x. It indicates how much the quantity increases or decreases for each unit increase in x.

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What does the term 'exponential growth' mean?

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Exponential growth refers to an increase that occurs at a rate proportional to the current value, leading to rapid growth over time.

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What does the term 'exponential decay' mean?

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Exponential decay refers to a decrease that occurs at a rate proportional to the current value, leading to rapid decline over time.