How do I calculate power plant capacity loss over 25 years?

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In summary, the conversation discusses two methods for calculating the production capacity of a power plant over a 25-year period, in which it loses 0.5% of its capacity each year. The first method involves multiplying the previous year's capacity by (100%-0.5%), while the second method subtracts 0.5% from the previous year's capacity. Both methods result in the same calculation, but it is important to note that the losses are cumulative. This means that in year 25, the production capacity will be 99.95% of the original capacity, or 24 if the plant runs at full capacity in the first year.
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clearway
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TL;DR Summary
Plant capacity degradation calculation
Hello,

I have a simple question and am hoping someone can help. I have a power plant that loses 0.5% production capacity per year for 25 years. When working with the plant capacity in terms of percentages, year 0 is defined as 100% capacity. For year 1 and each subsequent years, is it correct to take the current plant capacity percentage, and multiply it by (100%-0.5%)? Or do I subtract the 0.5% from the previous year?

Plant capacity:
Method 1:
Year 0 = 100%
Year 1 = Year 0 * (100%-0.5%)
Year 2 = Year 1 * (100%-0.5%)
etc

Method 2:
Year 0 = 100%
Year 1 = Year 0 - 0.5%
Year 2 = Year 1 - 0.5%

Thanks.
 
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  • #2
Percentage means only "divided by ##100##". So ##100\%=\frac{100}{100}=1##.

Now Year 1 = Year 0 ## \cdot (100\%-0.5\%)=##Year 0 ## \cdot (1-\frac{0.5}{100})=## Year 0 ## \cdot 1 - ##Year 0 ##\cdot \frac{1}{200}## which is what I think you meant by method 2. However, you haven't said from which quantity you want to take ##0.5\%## in method 2. The methods are the same if you subtract ##0.5\%## from Year 0, which makes sense as you lose this amount already in the first year.

What you also haven't said is, that the losses are cumulative, which your calculation is. For a constant loss you simply have ##99.95 \cdot ##Total every year.

In year ##25## you will have ##\operatorname{capacity}(25)=\operatorname{capacity}(0)\cdot (1-\frac{1}{200})^{25}## or ##24## if it runs on full capacity the first year.
 

Related to How do I calculate power plant capacity loss over 25 years?

1. What is simple arithmetic?

Simple arithmetic refers to basic mathematical operations such as addition, subtraction, multiplication, and division. These operations involve manipulating numbers to find a solution to a problem.

2. How do you solve a simple arithmetic question?

To solve a simple arithmetic question, you first need to identify the operation being used (addition, subtraction, multiplication, or division). Then, follow the appropriate steps to perform the operation and find the solution.

3. What are some common strategies for solving simple arithmetic questions?

Some common strategies for solving simple arithmetic questions include using mental math, using a calculator, breaking down the problem into smaller parts, and using the order of operations (PEMDAS).

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Yes, simple arithmetic is used in many real-life situations, such as calculating grocery bills, budgeting, and measuring ingredients for cooking. It is also used in more complex mathematical concepts and fields such as physics and engineering.

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Understanding simple arithmetic is important because it forms the foundation for more complex mathematical concepts and problem-solving skills. It is also used in everyday life and can help with making informed decisions and managing finances.

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