Writing Exponential Functions (Word Problems)

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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 represents growth or decay processes.

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What does it mean for a function to model exponential growth?

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A function models exponential growth if the base 'b' is greater than 1, indicating that the quantity increases over time.

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What does it mean for a function to model exponential decay?

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A function models exponential decay if the base 'b' is between 0 and 1, indicating that the quantity decreases over time.

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How do you identify the initial value in an exponential function?

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

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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.

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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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How do you convert a percentage decay rate to a decimal for use in an exponential function?

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To convert a percentage decay rate to a decimal, divide the percentage by 100. For example, a 30% decay rate becomes 0.30.

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What is the significance of the base in an exponential function?

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The base in an exponential function determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

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If a quantity triples every hour, how is this represented in an exponential function?

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This is represented as f(h) = a(3)^h, where 'a' is the initial quantity and 'h' is the number of hours.

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How do you write an exponential function for a quantity that decreases by a certain percentage?

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To write an exponential function for a quantity that decreases by a percentage, use the formula f(t) = a(1 - r)^t, where 'r' is the decay rate as a decimal.