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Sagot :
To solve this problem, let's start by determining the approximate quantity of liquefied natural gas (LNG) produced in May.
1. Initial Values from the Table:
- January: [tex]\( 88,280 \)[/tex] tons
- February: [tex]\( 89,781 \)[/tex] tons
- March: [tex]\( 91,307 \)[/tex] tons
2. Understanding the Monthly Increase:
The problem states that the quantity of LNG increases by [tex]\( 1.7\% \)[/tex] each month. This increase rate will be applied to the values incrementally to find the production for April and May.
3. Calculate April's Production:
Using March's production as the base (since it's the last value from the table):
[tex]\[ \text{April's production} = 91,307 \times (1 + 1.7\% ) \][/tex]
[tex]\[ \Rightarrow 91,307 \times 1.017 = 92,859.219 \, \text{tons} \][/tex]
4. Calculate May's Production:
Using April's production as the base:
[tex]\[ \text{May's production} = 92,859.219 \times (1 + 1.7\%) \][/tex]
[tex]\[ \Rightarrow 92,859.219 \times 1.017 = 94,437.825723 \, \text{tons} \][/tex]
Therefore, approximately [tex]\( 94,437.83 \)[/tex] tons of LNG will be produced in May.
5. Determine the Month to Reach 104.489 Tons:
Starting from May with [tex]\( 94,437.825723 \)[/tex] tons, we need to find out how many months it will take to reach [tex]\( 104,489 \)[/tex] tons. Every month, the production increases by [tex]\( 1.7\% \)[/tex].
Let’s calculate month-by-month until we reach [tex]\( 104,489 \)[/tex] tons.
- For June:
[tex]\[ 94,437.825723 \times 1.017 = 96,053.239 \, \text{tons} \][/tex]
- For July:
[tex]\[ 96,053.239 \times 1.017 = 97,692.144 \, \text{tons} \][/tex]
- For August:
[tex]\[ 97,692.144 \times 1.017 = 99,354.913 \, \text{tons} \][/tex]
- For September:
[tex]\[ 99,354.913 \times 1.017 = 101,041.952 \, \text{tons} \][/tex]
- For October:
[tex]\[ 101,041.952 \times 1.017 = 102,753.663 \, \text{tons} \][/tex]
- For November:
[tex]\[ 102,753.663 \times 1.017 = 104,489.515 \, \text{tons} \][/tex]
Therefore, approximately [tex]\( 104.489 \)[/tex] tons will be produced in November, which is the 11th month (starting from January as month 1).
Summarizing:
- Approximately [tex]\( 94,437.83 \)[/tex] tons of LNG will be produced in May.
- Approximately [tex]\( 104.489 \)[/tex] tons will be produced in November.
So, fill in the blanks as:
- Approximately [tex]\( \text{94,437.83} \)[/tex] tons of LNG will be produced in May.
- Approximately [tex]\( 104.489 \)[/tex] tons will be produced in [tex]\( \text{November} \)[/tex].
1. Initial Values from the Table:
- January: [tex]\( 88,280 \)[/tex] tons
- February: [tex]\( 89,781 \)[/tex] tons
- March: [tex]\( 91,307 \)[/tex] tons
2. Understanding the Monthly Increase:
The problem states that the quantity of LNG increases by [tex]\( 1.7\% \)[/tex] each month. This increase rate will be applied to the values incrementally to find the production for April and May.
3. Calculate April's Production:
Using March's production as the base (since it's the last value from the table):
[tex]\[ \text{April's production} = 91,307 \times (1 + 1.7\% ) \][/tex]
[tex]\[ \Rightarrow 91,307 \times 1.017 = 92,859.219 \, \text{tons} \][/tex]
4. Calculate May's Production:
Using April's production as the base:
[tex]\[ \text{May's production} = 92,859.219 \times (1 + 1.7\%) \][/tex]
[tex]\[ \Rightarrow 92,859.219 \times 1.017 = 94,437.825723 \, \text{tons} \][/tex]
Therefore, approximately [tex]\( 94,437.83 \)[/tex] tons of LNG will be produced in May.
5. Determine the Month to Reach 104.489 Tons:
Starting from May with [tex]\( 94,437.825723 \)[/tex] tons, we need to find out how many months it will take to reach [tex]\( 104,489 \)[/tex] tons. Every month, the production increases by [tex]\( 1.7\% \)[/tex].
Let’s calculate month-by-month until we reach [tex]\( 104,489 \)[/tex] tons.
- For June:
[tex]\[ 94,437.825723 \times 1.017 = 96,053.239 \, \text{tons} \][/tex]
- For July:
[tex]\[ 96,053.239 \times 1.017 = 97,692.144 \, \text{tons} \][/tex]
- For August:
[tex]\[ 97,692.144 \times 1.017 = 99,354.913 \, \text{tons} \][/tex]
- For September:
[tex]\[ 99,354.913 \times 1.017 = 101,041.952 \, \text{tons} \][/tex]
- For October:
[tex]\[ 101,041.952 \times 1.017 = 102,753.663 \, \text{tons} \][/tex]
- For November:
[tex]\[ 102,753.663 \times 1.017 = 104,489.515 \, \text{tons} \][/tex]
Therefore, approximately [tex]\( 104.489 \)[/tex] tons will be produced in November, which is the 11th month (starting from January as month 1).
Summarizing:
- Approximately [tex]\( 94,437.83 \)[/tex] tons of LNG will be produced in May.
- Approximately [tex]\( 104.489 \)[/tex] tons will be produced in November.
So, fill in the blanks as:
- Approximately [tex]\( \text{94,437.83} \)[/tex] tons of LNG will be produced in May.
- Approximately [tex]\( 104.489 \)[/tex] tons will be produced in [tex]\( \text{November} \)[/tex].
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