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 does it mean for a function to exhibit exponential growth?

Back

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

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

Back

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

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How can you identify an exponential decay function from its equation?

Back

An exponential decay function has a base 'b' that is between 0 and 1 (0 < b < 1).

Front

What is the y-intercept of an exponential function?

Back

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

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What is the common ratio in an exponential sequence?

Back

The common ratio in an exponential sequence is the factor by which each term is multiplied to get the next term.

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How do you determine if a graph represents exponential growth or decay?

Back

If the graph rises steeply as x increases, it represents exponential growth; if it falls steeply, it represents exponential decay.

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What is the formula for calculating the value of an exponential function at a given x?

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The value of an exponential function at a given x is calculated using f(x) = a * b^x.

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

Back

The base 'b' determines the rate of growth or decay; if b > 1, the function grows; if 0 < b < 1, the function decays.

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What is an example of an exponential growth scenario?

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An example of exponential growth is population growth, where the population increases by a percentage each year.