Exponential Growth & Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time. For example, if a population grows by 10% each year, it grows faster as the population increases.

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What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time. For example, radioactive substances decay exponentially.

Front

What is the general form of an exponential growth equation?

Back

Front

What is the general form of an exponential decay equation?

Back

Front

How do you find the growth rate from an exponential growth equation?

Back

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How do you find the decay rate from an exponential decay equation?

Back

Front

What does the base of an exponential function represent?

Back

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

Front

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

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The initial value 'a' represents the starting amount before any growth or decay occurs.

Front

If a population doubles every 5 years, what is the growth factor?

Back

The growth factor is 2, indicating that the population multiplies by 2 every 5 years.

Front

What is the relationship between growth rate and decay rate?

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The growth rate is the percentage increase, while the decay rate is the percentage decrease. They are complementary; for example, a 10% growth rate corresponds to a 10% decay rate in the context of the remaining quantity.