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Answer :
To solve the problem of determining the area that the moss will cover after 6 months, we can use the concept of exponential growth. In this scenario, the moss grows by multiplying its area by one and a half times each month.
1. Initial Setup:
- Start with the initial area covered by moss: 11 square centimeters.
2. Growth Rate:
- The growth rate is one and a half times each month. This means the area increases by a factor of 1.5 every month.
3. Time Period:
- Paul is observing the moss over a period of 6 months.
4. Calculation:
- To calculate the final area after 6 months, we can use the formula for exponential growth:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Number of Months}}
\][/tex]
- Plugging in the values:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
5. Result:
- When we calculate this, the final area comes out to be approximately 125.3 square centimeters.
Therefore, the correct answer is D. [tex]\(125.3 \, \text{cm}^2\)[/tex].
1. Initial Setup:
- Start with the initial area covered by moss: 11 square centimeters.
2. Growth Rate:
- The growth rate is one and a half times each month. This means the area increases by a factor of 1.5 every month.
3. Time Period:
- Paul is observing the moss over a period of 6 months.
4. Calculation:
- To calculate the final area after 6 months, we can use the formula for exponential growth:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Number of Months}}
\][/tex]
- Plugging in the values:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
5. Result:
- When we calculate this, the final area comes out to be approximately 125.3 square centimeters.
Therefore, the correct answer is D. [tex]\(125.3 \, \text{cm}^2\)[/tex].
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