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Answer :
To solve this problem, we need to determine how much area the moss will cover after 6 months given that it multiplies by one and a half times each month.
1. Understand the Initial Conditions:
The initial area covered by moss is 11 square centimeters.
2. Growth Factor Per Month:
Each month, the area covered by the moss increases by a factor of 1.5. This means that after each month, the new area is 1.5 times the area of the previous month.
3. Determine the Time Period:
We want to find out the area covered after 6 months.
4. Use the Growth Formula:
The formula to calculate the new area after a certain number of months, when the area multiplies by a constant factor each month, is:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Factor})^{\text{Number of Months}}
\][/tex]
5. Substitute the Values:
- Initial Area = 11 cm²
- Growth Factor per month = 1.5
- Number of Months = 6
So, the calculation will be:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
6. Calculate the Result:
After performing the calculation, we find that the final area covered by the moss is approximately 125.3 cm².
Therefore, the correct answer is option A: [tex]\( 125.3 \, \text{cm}^2 \)[/tex].
1. Understand the Initial Conditions:
The initial area covered by moss is 11 square centimeters.
2. Growth Factor Per Month:
Each month, the area covered by the moss increases by a factor of 1.5. This means that after each month, the new area is 1.5 times the area of the previous month.
3. Determine the Time Period:
We want to find out the area covered after 6 months.
4. Use the Growth Formula:
The formula to calculate the new area after a certain number of months, when the area multiplies by a constant factor each month, is:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Factor})^{\text{Number of Months}}
\][/tex]
5. Substitute the Values:
- Initial Area = 11 cm²
- Growth Factor per month = 1.5
- Number of Months = 6
So, the calculation will be:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
6. Calculate the Result:
After performing the calculation, we find that the final area covered by the moss is approximately 125.3 cm².
Therefore, the correct answer is option A: [tex]\( 125.3 \, \text{cm}^2 \)[/tex].
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