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Answer :
To find out how much area the moss will cover after 6 months, we need to consider the initial area covered by moss and the growth rate of the moss each month.
1. Initial Area: The moss initially covers an area of 11 square centimeters.
2. Growth Rate: The moss grows by one and a half times (1.5 times) every month.
3. Time Period: We need to know how much the moss grows over the course of 6 months.
Let's calculate the final area:
- Every month, the moss area is multiplied by 1.5. So, after 1 month, the area becomes:
[tex]\[ \text{Area after 1 month} = 11 \times 1.5 \][/tex]
- After 2 months, the area becomes:
[tex]\[ \text{Area after 2 months} = (11 \times 1.5) \times 1.5 = 11 \times (1.5^2) \][/tex]
- Continuing this process for 6 months, the area becomes:
[tex]\[ \text{Area after 6 months} = 11 \times (1.5^6) \][/tex]
Using this calculation, the area after 6 months is approximately 125.3 square centimeters.
Therefore, the correct answer is:
B. 125.3 cm²
1. Initial Area: The moss initially covers an area of 11 square centimeters.
2. Growth Rate: The moss grows by one and a half times (1.5 times) every month.
3. Time Period: We need to know how much the moss grows over the course of 6 months.
Let's calculate the final area:
- Every month, the moss area is multiplied by 1.5. So, after 1 month, the area becomes:
[tex]\[ \text{Area after 1 month} = 11 \times 1.5 \][/tex]
- After 2 months, the area becomes:
[tex]\[ \text{Area after 2 months} = (11 \times 1.5) \times 1.5 = 11 \times (1.5^2) \][/tex]
- Continuing this process for 6 months, the area becomes:
[tex]\[ \text{Area after 6 months} = 11 \times (1.5^6) \][/tex]
Using this calculation, the area after 6 months is approximately 125.3 square centimeters.
Therefore, the correct answer is:
B. 125.3 cm²
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