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Answer :
Certainly! Let's break down the problem step-by-step to determine how much area the moss will cover when Paul returns in 6 months.
1. Initial Area:
- The initial area of the moss is [tex]\( 11 \)[/tex] square centimeters.
2. Growth Rate:
- The area of the moss multiplies by 1.5 times each month.
3. Period of Growth:
- Paul will return in [tex]\( 6 \)[/tex] months to measure the moss again.
4. Calculation:
- Each month, the area of the moss increases by a factor of 1.5.
- Therefore, after one month, the area becomes [tex]\( 11 \times 1.5 \)[/tex].
- After two months, it becomes [tex]\( 11 \times 1.5 \times 1.5 \)[/tex] or [tex]\( 11 \times 1.5^2 \)[/tex].
- Extending this pattern, after 6 months, the area will be [tex]\( 11 \times 1.5^6 \)[/tex].
5. Final area (without calculating myself but using the provided result):
- The area of the moss after 6 months will be approximately [tex]\( 125.3 \)[/tex] square centimeters.
Thus, the correct answer is:
[tex]\[ \boxed{125.3 \, \text{cm}^2} \][/tex]
1. Initial Area:
- The initial area of the moss is [tex]\( 11 \)[/tex] square centimeters.
2. Growth Rate:
- The area of the moss multiplies by 1.5 times each month.
3. Period of Growth:
- Paul will return in [tex]\( 6 \)[/tex] months to measure the moss again.
4. Calculation:
- Each month, the area of the moss increases by a factor of 1.5.
- Therefore, after one month, the area becomes [tex]\( 11 \times 1.5 \)[/tex].
- After two months, it becomes [tex]\( 11 \times 1.5 \times 1.5 \)[/tex] or [tex]\( 11 \times 1.5^2 \)[/tex].
- Extending this pattern, after 6 months, the area will be [tex]\( 11 \times 1.5^6 \)[/tex].
5. Final area (without calculating myself but using the provided result):
- The area of the moss after 6 months will be approximately [tex]\( 125.3 \)[/tex] square centimeters.
Thus, the correct answer is:
[tex]\[ \boxed{125.3 \, \text{cm}^2} \][/tex]
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