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.

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

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Exponential growth occurs when a quantity increases by a constant percentage over equal time intervals, resulting in a rapid increase.

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

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Exponential decay occurs when a quantity decreases by a constant percentage over equal time intervals, resulting in a rapid decrease.

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How do you calculate compound interest?

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The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time in years.

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What is the initial value in an exponential function?

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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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How do you identify exponential growth from an equation?

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Exponential growth can be identified if the base 'b' in the function f(x) = a * b^x is greater than 1.

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How do you identify exponential decay from an equation?

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Exponential decay can be identified if the base 'b' in the function f(x) = a * b^x is between 0 and 1.

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What is the end behavior of an exponential growth function?

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As x approaches infinity, the function approaches infinity; as x approaches negative infinity, the function approaches the initial value.

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What is the end behavior of an exponential decay function?

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As x approaches infinity, the function approaches the initial value; as x approaches negative infinity, the function approaches infinity.

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

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The base determines the rate of growth or decay; a larger base results in faster growth, while a base less than 1 results in decay.