Writing and Interpreting 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.

Front

What does the initial value in an exponential function represent?

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The initial value is the value of the function when x = 0, represented by 'a' in the function f(x) = a(b)^x.

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What is the growth factor in an exponential function?

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The growth factor is the base 'b' in the function f(x) = a(b)^x when b > 1, indicating how much the function increases.

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What is the decay factor in an exponential function?

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The decay factor is the base 'b' in the function f(x) = a(b)^x when 0 < b < 1, indicating how much the function decreases.

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How do you identify the asymptote of an exponential function?

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The horizontal asymptote of an exponential function f(x) = a(b)^x is typically y = 0, as the function approaches this line but never touches it.

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What is the formula for exponential growth?

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

Front

If a quantity doubles every period, what is the growth factor?

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The growth factor is 2, as the quantity increases by a factor of 2 each period.

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If a quantity halves every period, what is the decay factor?

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The decay factor is 0.5, as the quantity decreases to half its value each period.

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

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To convert a percentage increase 'p%' to a growth factor, use the formula: growth factor = 1 + (p/100).