Exponential Functions Review

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What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a(b^x), where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent.

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What is exponential growth?

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Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, often represented by functions where the base of the exponent is greater than 1.

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What is exponential decay?

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Exponential decay occurs when a quantity decreases by a consistent percentage over time, often represented by functions where the base of the exponent is between 0 and 1.

Front

How can you identify an exponential function?

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An exponential function can be identified by its variable being in the exponent and having a constant base that is positive and not equal to 1.

Front

What is the difference between linear and exponential functions?

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Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases multiplicatively.

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What does the base of an exponential function indicate?

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The base of an exponential function indicates the growth or decay factor; if the base is greater than 1, it represents growth, and if it is between 0 and 1, it represents decay.

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What is an example of exponential growth?

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An example of exponential growth is the population of bacteria that doubles every hour.

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What is an example of exponential decay?

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An example of exponential decay is the depreciation of a car's value, which decreases by a certain percentage each year.

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What does it mean if a function is linear?

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A linear function is a function that graphs to a straight line and has a constant rate of change, typically represented in the form y = mx + b.

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How do you determine if a function is exponential or linear?

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To determine if a function is exponential or linear, check if the variable is in the exponent (exponential) or if it is multiplied by a constant (linear).