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 a positive real number, and 'x' is the exponent.

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What is the difference between exponential growth and decay?

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Exponential growth occurs when the base 'b' in the function f(x) = a * b^x is greater than 1, while exponential decay occurs when 'b' is between 0 and 1.

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What is the decay factor in an exponential decay model?

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The decay factor is the value by which the quantity decreases in each time period, calculated as 1 - decay rate.

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How do you identify an exponential decay function from a formula?

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An exponential decay function can be identified by a formula of the form A = A0 * (1 - r)^t, where A0 is the initial amount, r is the decay rate, and t is time.

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What is the explicit formula for a geometric sequence?

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The explicit formula for a geometric sequence is a_n = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.

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How do you find the common ratio in a geometric sequence?

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The common ratio 'r' can be found by dividing any term by the previous term in the sequence.

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What is the formula for exponential growth?

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The formula for exponential growth is A = A0 * (1 + r)^t, where A0 is the initial amount, r is the growth rate, and t is time.

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What does it mean for a function to be exponential?

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A function is considered exponential if it can be expressed in the form f(x) = a * b^x, where 'b' is a constant greater than 0.

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How do you write an explicit formula for a sequence given its terms?

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To write an explicit formula for a sequence, identify the pattern in the terms and express it in the form a_n = a * r^(n-1) or similar.

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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.