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Answer :
To solve the problem of determining how much area the moss will cover after 6 months, we know that the moss grows by one and a half times each month.
1. Initial Area: The initial area covered by moss is 11 square centimeters.
2. Growth Rate: The growth rate is 1.5 times the current area every month.
3. Time Period: We are asked to find the moss-covered area after 6 months.
To find the final area after 6 months, you can follow these steps:
- Each month, the area is multiplied by 1.5, so after 1 month, the area will be [tex]\(11 \times 1.5\)[/tex].
- After 2 months, it will be [tex]\((11 \times 1.5) \times 1.5\)[/tex].
- Similarly, after 6 months, the area will be multiplied by 1.5 each month for 6 months.
This can be expressed mathematically as:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Number of Months}}
\][/tex]
Substitute the given numbers:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
When you calculate this using the above formula, the final area covered by the moss after 6 months will be approximately 125.3 square centimeters.
Therefore, the correct answer is A. 125.3 cm².
1. Initial Area: The initial area covered by moss is 11 square centimeters.
2. Growth Rate: The growth rate is 1.5 times the current area every month.
3. Time Period: We are asked to find the moss-covered area after 6 months.
To find the final area after 6 months, you can follow these steps:
- Each month, the area is multiplied by 1.5, so after 1 month, the area will be [tex]\(11 \times 1.5\)[/tex].
- After 2 months, it will be [tex]\((11 \times 1.5) \times 1.5\)[/tex].
- Similarly, after 6 months, the area will be multiplied by 1.5 each month for 6 months.
This can be expressed mathematically as:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Number of Months}}
\][/tex]
Substitute the given numbers:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
When you calculate this using the above formula, the final area covered by the moss after 6 months will be approximately 125.3 square centimeters.
Therefore, the correct answer is A. 125.3 cm².
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