## Decay Factor

### In mathematics, the concept of decay factor is often used in exponential decay models

In mathematics, the concept of decay factor is often used in exponential decay models. It represents the rate at which a quantity decreases over time.

In exponential decay, the amount of a substance or value decreases exponentially over time, following a specific pattern. The decay factor, denoted by the letter “r,” is a constant value between 0 and 1. It defines the rate at which the quantity decreases.

To understand the concept of decay factor, let’s consider an example. Suppose you have an initial quantity of 100 units that is decreasing by 10% every year. In this case, the decay factor “r” would be 0.10 (10% expressed as a decimal).

To calculate the value after a certain number of years, you can use the formula:

Final value = Initial value × (1 – r)^n

where:

– Initial value is the starting quantity

– r is the decay factor

– n is the number of time periods

For our example, let’s calculate the value after 5 years:

Final value = 100 × (1 – 0.10)^5

Final value = 100 × (0.90)^5

Final value ≈ 59.05

Therefore, after 5 years, the quantity would have decreased to approximately 59.05 units.

It’s important to note that the value of the decay factor determines the speed of decay. If the decay factor is closer to 1, the quantity will decrease slowly, while a decay factor closer to 0 will result in a rapid decline.

In summary, the decay factor describes the rate at which a quantity decreases in exponential decay. It is a constant value between 0 and 1, with smaller values representing a faster decay. The formula Final value = Initial value × (1 – r)^n is used to calculate the value after a certain number of time periods.

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