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. It shows rapid growth or decay.

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What does exponential growth mean?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, leading to a rapid increase.

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What does exponential decay mean?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease.

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What is the y-intercept of an exponential function?

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The y-intercept is the value of the function when x = 0, representing the initial amount before any growth or decay occurs.

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How can you identify exponential growth on a graph?

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Exponential growth is identified by a curve that rises steeply as x increases, indicating that the quantity is increasing rapidly.

Front

How can you identify exponential decay on a graph?

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Exponential decay is identified by a curve that falls steeply as x increases, indicating that the quantity is decreasing rapidly.

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What does the base of an exponential function represent?

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The base of an exponential function indicates the growth or decay factor. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

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What is the formula for exponential growth?

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The formula for exponential growth is f(t) = a * (1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

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What is the formula for exponential decay?

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The formula for exponential decay is f(t) = a * (1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

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If a population is modeled by f(t) = 100(1.05)^t, what does 1.05 represent?

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In this model, 1.05 represents a 5% growth rate per time unit.