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Answer :
To solve this problem, we need to calculate the area of moss growth over a period of 6 months. We start with an initial area of 11 square centimeters and the moss grows at a rate of multiplying by one and a half times each month.
Here's how we can determine the total area after 6 months:
1. Initial Area: We know that the initial area covered by moss is 11 square centimeters.
2. Growth Rate: The moss increases by one and a half times, meaning for each month, the area is multiplied by 1.5.
3. Number of Months: We are calculating the growth over a period of 6 months.
4. Calculate the Final Area:
- Use the formula for exponential growth:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Number of Months}}
\][/tex]
- Plug in the known values:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
5. Calculate Step-by-Step:
- First, compute [tex]\( (1.5)^6 \)[/tex].
- Multiply this result by the initial area of 11 cm² to find the final area.
The final result is approximately 125.3 cm².
Hence, the correct answer is:
C. [tex]\(125.3 \, \text{cm}^2\)[/tex]
Here's how we can determine the total area after 6 months:
1. Initial Area: We know that the initial area covered by moss is 11 square centimeters.
2. Growth Rate: The moss increases by one and a half times, meaning for each month, the area is multiplied by 1.5.
3. Number of Months: We are calculating the growth over a period of 6 months.
4. Calculate the Final Area:
- Use the formula for exponential growth:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Number of Months}}
\][/tex]
- Plug in the known values:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
5. Calculate Step-by-Step:
- First, compute [tex]\( (1.5)^6 \)[/tex].
- Multiply this result by the initial area of 11 cm² to find the final area.
The final result is approximately 125.3 cm².
Hence, the correct answer is:
C. [tex]\(125.3 \, \text{cm}^2\)[/tex]
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