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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. It represents growth or decay at a constant percentage rate.

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What is the difference between linear and exponential functions?

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Linear functions increase or decrease by a constant amount (e.g., y = mx + b), while exponential functions increase or decrease by a constant factor (e.g., y = a * b^x).

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What does it mean for a function to multiply the same number each time?

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This describes an exponential function, where the output is multiplied by a constant factor for each unit increase in the input.

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What is the starting point of an exponential function?

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The starting point of an exponential function is the value of 'a' in the function f(x) = a * b^x, which represents the initial value when x = 0.

Tags

CCSS.HSF-IF.C.7E

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How can you identify an exponential function from a table of values?

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If the differences between consecutive outputs are not constant but the ratios of consecutive outputs are constant, the function is exponential.

Tags

CCSS.HSF-LE.A.1A

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What is the general form of an exponential function?

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The general form is f(x) = a * b^x, where 'a' is the initial value and 'b' is the base that determines the growth or decay rate.

Tags

CCSS.HSF.LE.A.2

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What does the base 'b' represent in an exponential function?

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The base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

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CCSS.HSF-IF.C.8B

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How do you determine if a graph is exponential?

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A graph is exponential if it shows a rapid increase or decrease and has a characteristic curve that is not a straight line.

Tags

CCSS.HSF-IF.C.7E

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What is the pattern in an exponential growth table?

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In an exponential growth table, the values increase by multiplying by a constant factor, leading to larger gaps between consecutive values as x increases.

Tags

CCSS.HSF-LE.A.1A

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What is an example of an exponential function?

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An example is f(x) = 2^x, which doubles the output for each increase of 1 in x.