Exponential Growth and Decay

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What is Exponential Growth?

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Exponential growth occurs when the increase in a quantity is proportional to its current value, leading to growth at an increasing rate. For example, if a population grows by 10% each year, it grows faster each year.

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What is Exponential Decay?

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Exponential decay is the decrease in a quantity at a rate proportional to its current value, leading to a rapid decline. For example, radioactive substances decay over time at a rate proportional to their current amount.

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What is the formula for Exponential Growth?

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The formula 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 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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What is a Growth Factor?

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The growth factor is the amount by which a quantity increases in each time period, calculated as (1 + r) for growth.

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What is a Decay Factor?

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The decay factor is the amount by which a quantity decreases in each time period, calculated as (1 - r) for decay.

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How do you calculate the decay factor from a percentage?

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The decay factor is calculated as (1 - r), where 'r' is the decay rate expressed as a decimal. For example, an 8% decay rate gives a decay factor of 0.92.

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What does it mean if a function is linear?

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A linear function has a constant rate of change and can be represented by a straight line on a graph. It follows the form y = mx + b.

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What does it mean if a function is exponential?

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An exponential function has a variable rate of change and can be represented by a curve on a graph. It follows the form y = ab^x.

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

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The base determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.