Exponential Functions

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What is an exponential function?

Back

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 base of an exponential function?

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The base of an exponential function is the constant 'b' in the function f(x) = a * b^x, which determines the rate of growth or decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to rapid increases over time.

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CCSS.HSF-LE.A.1A

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What is exponential decay?

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Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to a rapid decrease over time.

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CCSS.HSF-IF.C.8B

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How do you solve an exponential equation?

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To solve an exponential equation, you can take the logarithm of both sides or rewrite the equation in a form that allows for easier manipulation.

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What is the formula for continuous compound interest?

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The formula for continuous compound interest is A = Pe^(rt), where A is the amount, P is the principal, r is the rate, and t is time.

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What is the value of 2^3?

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2^3 = 8.

Tags

CCSS.6.EE.A.1

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If f(x) = 3(2^x), what is f(4)?

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f(4) = 3(2^4) = 3(16) = 48.

Tags

CCSS.HSF-IF.C.8B

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What is the inverse of an exponential function?

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The inverse of an exponential function is a logarithmic function.

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CCSS.HSF-BF.B.4A

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How do you express 27^(2x) = 3^(x-7) in terms of the same base?

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27 can be expressed as 3^3, so 27^(2x) = (3^3)^(2x) = 3^(6x). Thus, the equation becomes 3^(6x) = 3^(x-7).