Answer:
The given decay rate of 11.6% per week is already the weekly decay rate. Therefore, the weekly decay rate of the quantity is 11.6%.
Explanation:
When we talk about decay, we are referring to a gradual decrease or reduction in the quantity over time. In this scenario, we are presented with a situation where a quantity is experiencing weekly decay at a continuous rate of 11.6%. To understand the magnitude and significance of this decay rate, we need to delve deeper into the concept of continuous decay.
Continuous decay is a mathematical concept that models the continuous decrease or decline of a quantity over time. It assumes that the quantity is decreasing at a constant rate, meaning the change in quantity is proportional to the current amount, regardless of the time interval considered. This is in contrast to discrete decay, which occurs in discrete or interval steps, such as daily or monthly.
In our case, we are specifically concerned with the decay rate per week. The decay rate represents the percentage decrease in the quantity over a given time period. It indicates how much of the quantity is lost per unit of time. In this context, a decay rate of 11.6% per week means that the quantity decreases by 11.6% of its current value every week.
To illustrate this, let's consider an initial quantity of, say, 100 units. Applying the decay rate of 11.6% per week, we first calculate the amount lost each week by multiplying the current quantity by the decay rate: 100 units * 0.116 = 11.6 units. This means that after the first week, 11.6 units would be decayed, leaving us with 100 - 11.6 = 88.4 units.
Moving on to the second week, we repeat the process. Starting with the new quantity of 88.4 units, we multiply it by the decay rate of 11.6%: 88.4 units * 0.116 = 10.2496 units. Therefore, in the second week, an additional 10.2496 units would decay, resulting in 88.4 - 10.2496 = 78.1504 units.
By repeating these calculations each week, we observe that the quantity continues to decay by approximately 11.6% of its current value. This is due to the continuous nature of the decay rate, where the decrease in quantity is continuously proportional to the current amount.
Hence, we can conclude that the weekly decay rate of the quantity is indeed 11.6%, and this verbose explanation aims to provide a detailed understanding of why this is the case in the context of continuous decay.
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