Writing 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 does the base of an exponential function represent in the context of growth or decay?

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The base of an exponential function indicates the growth or decay factor. If the base is greater than 1, it represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

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How do you write an exponential decay function?

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An exponential decay function can be written in the form 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 decay rate in the context of exponential decay?

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The decay rate is the fraction of the quantity that decreases over a specific time period, often expressed as a percentage.

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How can you determine the amount remaining after a certain time using an exponential function?

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You can determine the amount remaining by substituting the time value into the exponential function and calculating the result.

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What is the significance of the initial value in an exponential function?

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The initial value represents the starting amount before any growth or decay occurs.

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What does the term 'half-life' refer to in exponential decay?

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Half-life is the time required for a quantity to reduce to half its initial value in an exponential decay process.

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How do you convert a decay rate into a base for an exponential function?

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To convert a decay rate 'r' into a base, use the formula base = 1 - r.

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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(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 difference between exponential growth and exponential decay?

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Exponential growth occurs when a quantity increases over time, while exponential decay occurs when a quantity decreases over time.