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What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase. For example, if a population grows by 5% each year, it is experiencing exponential growth.

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What is exponential decay?

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Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease. For example, if a radioactive substance decays by 10% each year, it is experiencing exponential decay.

Front

Identify the general form of an exponential growth function.

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Front

Identify the general form of an exponential decay function.

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Front

What does the base 'b' represent in an exponential function?

Back

In an exponential function, the base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor. It determines how quickly the function increases or decreases.

Front

How can you determine if a function represents exponential growth or decay from its equation?

Back

If the base of the exponent is greater than 1, the function represents exponential growth. If the base is between 0 and 1, it represents exponential decay.

Front

What is the significance of the initial value 'a' in an exponential function?

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How does the graph of an exponential growth function behave?

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The graph of an exponential growth function rises steeply as x increases, showing a rapid increase in value.

Front

How does the graph of an exponential decay function behave?

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The graph of an exponential decay function falls steeply as x increases, showing a rapid decrease in value.

Front

What is an example of a real-world situation that demonstrates exponential growth?

Back

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