Exponential Functions

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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 the 'a' represent in an exponential function?

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In an exponential function, 'a' represents the y-intercept, which is the value of the function when x = 0.

Tags

CCSS.HSF-IF.C.7E

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What is the common ratio in an exponential function?

Back

The common ratio is the factor by which the function's value multiplies for each unit increase in x.

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How does an exponential function differ from a linear function?

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An exponential function grows or decays at a rate proportional to its current value, while a linear function grows at a constant rate.

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What is the general shape of the graph of an exponential function?

Back

The graph of an exponential function is a curve that either rises steeply (if b > 1) or falls steeply (if 0 < b < 1) as x increases.

Tags

CCSS.HSF-IF.C.7E

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What does it mean if an amount triples each year?

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It means the growth is exponential, as the amount increases by a factor of 3 for each unit of time.

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CCSS.HSF-LE.A.1A

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If an amount increases by $10 each year, what type of function is this?

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This is a linear function, as the increase is constant.

Tags

CCSS.8.F.A.3

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What is the rate of change in an exponential function?

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The rate of change in an exponential function is not constant; it increases or decreases exponentially based on the current value.

Tags

CCSS.HSF-IF.C.8B

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What is the y-intercept of the function f(x) = 2 * 3^x?

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The y-intercept is 2, which is the value of the function when x = 0.

Tags

CCSS.HSF-IF.C.7E

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What does it mean for a function to be neither linear nor exponential?

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It means the function does not exhibit constant growth (linear) or proportional growth (exponential), possibly showing a different type of relationship.