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Answer :
To solve this problem, we need to determine how much area will be covered by moss after 6 months, given it multiplies by one and a half times each month.
1. Initial Area: The initial area covered by the moss is 11 square centimeters.
2. Growth Factor: Each month, the area of moss grows by one and a half times, which means a growth factor of 1.5.
3. Time Period: The growth happens over a period of 6 months.
4. Calculating the Final Area:
- For each month, the area covered by moss is multiplied by the monthly growth factor.
- To find the area after 6 months, you multiply the initial area by the growth factor raised to the power of the number of months.
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Factor})^{\text{Number of Months}}
\][/tex]
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
5. Result: After calculating, the final area covered by moss is approximately 125.3 square centimeters.
Therefore, the correct answer is:
B. [tex]\(125.3 \, \text{cm}^2\)[/tex]
1. Initial Area: The initial area covered by the moss is 11 square centimeters.
2. Growth Factor: Each month, the area of moss grows by one and a half times, which means a growth factor of 1.5.
3. Time Period: The growth happens over a period of 6 months.
4. Calculating the Final Area:
- For each month, the area covered by moss is multiplied by the monthly growth factor.
- To find the area after 6 months, you multiply the initial area by the growth factor raised to the power of the number of months.
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Factor})^{\text{Number of Months}}
\][/tex]
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
5. Result: After calculating, the final area covered by moss is approximately 125.3 square centimeters.
Therefore, the correct answer is:
B. [tex]\(125.3 \, \text{cm}^2\)[/tex]
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