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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 the base (a positive real number), and 'x' is the exponent.

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What does it mean for a function to have a growth factor?

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A growth factor indicates that the function's value increases as the input increases. In an exponential function, if the base 'b' is greater than 1, it represents growth.

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What does it mean for a function to have a decay factor?

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A decay factor indicates that the function's value decreases as the input increases. In an exponential function, if the base 'b' is between 0 and 1, it represents decay.

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How do you determine the transformation of a function?

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Transformations can be determined by analyzing changes in the function's equation, such as shifts (horizontal or vertical) and stretches or compressions.

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What is a vertical shift in a function?

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A vertical shift occurs when a constant is added or subtracted from the function, moving it up or down on the graph.

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What is a horizontal shift in a function?

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A horizontal shift occurs when a constant is added or subtracted from the input variable, moving the graph left or right.

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How do you calculate the population after a certain time with exponential growth?

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Use the formula y = a(2^(t/T)), where 'a' is the initial amount, 't' is the total time, and 'T' is the time it takes for the population to double.

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What is the doubling time in exponential growth?

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The doubling time is the period it takes for a quantity to double in size or value, often used in population growth models.

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What is the formula for exponential decay?

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The formula for exponential decay is f(t) = a * e^(-kt), where 'a' is the initial amount, 'k' is the decay constant, and 't' is time.

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What is a vertical stretch in a function?

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A vertical stretch occurs when the output of the function is multiplied by a factor greater than 1, making the graph taller.