Exponential Functions Test 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 consistent percentage over equal intervals of time, represented by a base greater than 1 in the function.

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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 consistent percentage over equal intervals of time, represented by a base between 0 and 1 in the function.

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How do you write an expression for exponential growth?

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An expression for exponential growth can be written as y = 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 write an expression for exponential decay?

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An expression for exponential decay can be written as y = 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 the nth term of a geometric sequence?

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The nth term of a geometric sequence can be expressed as a_n = a * r^(n-1), where 'a' is the first term, 'r' is the common ratio, and 'n' is the term number.

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What is the difference between a geometric sequence and an arithmetic sequence?

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A geometric sequence has a constant ratio between consecutive terms, while an arithmetic sequence has a constant difference between consecutive terms.

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How do you determine if a function is exponential growth or decay based on its base?

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If the base 'b' is greater than 1, the function represents exponential growth. If the base 'b' is between 0 and 1, it represents exponential decay.

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What is the initial value in an exponential function?

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The initial value in an exponential function 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 express a 35% increase in an exponential function?

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A 35% increase can be expressed as y = a(1.35)^t, where 'a' is the initial amount and 't' is time.