Select The Correct Answer From Each Drop-down Menu.The Approximate Quantity Of Liquefied Natural Gas (LNG), In Tons, Produced By An Energy Company Increases By $1.7\%$ Each Month As Shown In The Table
Introduction
In this problem, we are given a table showing the approximate quantity of liquefied natural gas (LNG) produced by an energy company. The quantity increases by 1.7% each month. We need to select the correct answer from each drop-down menu, which represents the quantity of LNG produced at the end of each month.
The Problem
| Month | Quantity (tons) |
|---|---|
| 0 | 100 |
| 1 | 107.00 |
| 2 | 111.49 |
| 3 | 116.3413 |
| 4 | 122.109469 |
| 5 | 129.17651183 |
| 6 | 137.311511111 |
| 7 | 146.623511111 |
| 8 | 156.283511111 |
| 9 | 166.221511111 |
| 10 | 176.535511111 |
| 11 | 187.323511111 |
| 12 | 198.471511111 |
Calculating the Quantity of LNG Produced
To calculate the quantity of LNG produced at the end of each month, we can use the formula for compound interest:
A = P(1 + r)^n
where:
- A is the final quantity of LNG produced
- P is the initial quantity of LNG produced (100 tons)
- r is the monthly increase rate (1.7% or 0.017)
- n is the number of months
We can plug in the values for each month to calculate the quantity of LNG produced.
Month 1
A = 100(1 + 0.017)^1 A = 100(1.017) A = 107.00
Month 2
A = 107.00(1 + 0.017)^1 A = 107.00(1.017) A = 111.49
Month 3
A = 111.49(1 + 0.017)^1 A = 111.49(1.017) A = 116.3413
Month 4
A = 116.3413(1 + 0.017)^1 A = 116.3413(1.017) A = 122.109469
Month 5
A = 122.109469(1 + 0.017)^1 A = 122.109469(1.017) A = 129.17651183
Month 6
A = 129.17651183(1 + 0.017)^1 A = 129.17651183(1.017) A = 137.311511111
Month 7
A = 137.311511111(1 + 0.017)^1 A = 137.311511111(1.017) A = 146.623511111
Month 8
A = 146.623511111(1 + 0.017)^1 A = 146.623511111(1.017) A = 156.283511111
Month 9
A = 156.283511111(1 + 0.017)^1 A = 156.283511111(1.017) A = 166.221511111
Month 10
A = 166.221511111(1 + 0.017)^1 A = 166.221511111(1.017) A = 176.535511111
Month 11
A = 176.535511111(1 + 0.017)^1 A = 176.535511111(1.017) A = 187.323511111
Month 12
A = 187.323511111(1 + 0.017)^1 A = 187.323511111(1.017) A = 198.471511111
Conclusion
In this problem, we calculated the quantity of LNG produced at the end of each month using the formula for compound interest. We can see that the quantity of LNG produced increases by 1.7% each month, resulting in a significant increase in the quantity of LNG produced over time.
Select the Correct Answer from Each Drop-Down Menu
| Month | Quantity (tons) |
|---|---|
| 0 | 100 |
| 1 | 107.00 |
| 2 | 111.49 |
| 3 | 116.3413 |
| 4 | 122.109469 |
| 5 | 129.17651183 |
| 6 | 137.311511111 |
| 7 | 146.623511111 |
| 8 | 156.283511111 |
| 9 | 166.221511111 |
| 10 | 176.535511111 |
| 11 | 187.323511111 |
| 12 | 198.471511111 |
Frequently Asked Questions
Q1: What is liquefied natural gas (LNG)?
A1: Liquefied natural gas (LNG) is a type of natural gas that has been cooled to a liquid state, making it easier to transport and store. LNG is a clean-burning fuel that is used as a substitute for traditional fossil fuels.
Q2: How is LNG produced?
A2: LNG is produced by cooling natural gas to a temperature of around -162°C, at which point it becomes a liquid. This process involves several steps, including:
- Extraction of natural gas from underground reservoirs
- Processing of the natural gas to remove impurities and contaminants
- Cooling of the natural gas to a liquid state
Q3: What is the significance of the 1.7% monthly increase in LNG production?
A3: The 1.7% monthly increase in LNG production represents the rate at which the quantity of LNG produced increases each month. This increase is due to the compounding effect of the monthly growth rate, which results in a significant increase in the quantity of LNG produced over time.
Q4: How can I calculate the quantity of LNG produced at the end of each month?
A4: To calculate the quantity of LNG produced at the end of each month, you can use the formula for compound interest:
A = P(1 + r)^n
where:
- A is the final quantity of LNG produced
- P is the initial quantity of LNG produced (100 tons)
- r is the monthly increase rate (1.7% or 0.017)
- n is the number of months
Q5: What is the significance of the table showing the quantity of LNG produced at the end of each month?
A5: The table shows the quantity of LNG produced at the end of each month, based on the 1.7% monthly increase in production. This table can be used to calculate the quantity of LNG produced at the end of each month, and to visualize the growth in LNG production over time.
Q6: How can I use the information in the table to make predictions about future LNG production?
A6: You can use the information in the table to make predictions about future LNG production by extrapolating the growth rate of 1.7% per month. This can be done by using the formula for compound interest, and by adjusting the number of months to reflect the desired time period.
Q7: What are the implications of the growth in LNG production for the energy industry?
A7: The growth in LNG production has significant implications for the energy industry, including:
- Increased competition for traditional fossil fuels
- Reduced greenhouse gas emissions due to the cleaner-burning nature of LNG
- Increased demand for LNG infrastructure, including storage facilities and transportation networks
Q8: How can I use the information in this article to make informed decisions about LNG production?
A8: You can use the information in this article to make informed decisions about LNG production by:
- Understanding the growth rate of LNG production and its implications for the energy industry
- Calculating the quantity of LNG produced at the end of each month using the formula for compound interest
- Visualizing the growth in LNG production over time using the table provided
Conclusion
In this article, we have provided answers to frequently asked questions about liquefied natural gas (LNG) production, including the significance of the 1.7% monthly increase in production, and the implications of the growth in LNG production for the energy industry. We have also provided a table showing the quantity of LNG produced at the end of each month, and a formula for calculating the quantity of LNG produced at the end of each month using the formula for compound interest.