Exponential Growth and Decay

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What is exponential growth?

Back

Exponential growth occurs when the increase in a quantity is proportional to its current value, leading to growth at a constant percentage rate over time.

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What is exponential decay?

Back

Exponential decay is the process by which a quantity decreases at a rate proportional to its current value, resulting in a rapid decrease initially that slows over time.

Front

What is the general formula for exponential growth?

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The general formula for exponential growth is y = 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 general formula for exponential decay?

Back

The general formula for exponential decay is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

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How do you calculate the remaining amount after a certain time in exponential decay?

Back

To calculate the remaining amount after time 't' in exponential decay, use the formula y = a(1 - r)^t, where 'a' is the initial amount and 'r' is the decay rate.

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What is a growth factor?

Back

A growth factor is a multiplier used to calculate the new value after growth; it is equal to 1 plus the growth rate (expressed as a decimal).

Front

What is a decay factor?

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A decay factor is a multiplier used to calculate the new value after decay; it is equal to 1 minus the decay rate (expressed as a decimal).

Front

If a substance decays at a rate of 20% per hour, what is the decay factor?

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The decay factor is 0.8, calculated as 1 - 0.20.

Front

How do you determine the amount remaining after multiple periods of decay?

Back

To determine the amount remaining after multiple periods of decay, apply the decay formula repeatedly or use the formula y = a(1 - r)^t.

Front

What is the significance of the base in an exponential function?

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