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Answer :
To solve the problem of how much area the moss will cover when Paul returns, we need to understand exponential growth. The concept here is that the moss area grows by a factor of one and a half (or 1.5 times) every month. Here's how you can calculate the area covered by the moss after 6 months:
1. Understand the Initial Conditions:
- The initial area of moss is 11 square centimeters.
2. Growth Factor per Month:
- Each month, the area of moss increases by a factor of 1.5.
3. Determine the Time Period:
- Paul will check the moss after 6 months.
4. Calculate the Final Area:
- To find out how much the moss grows, multiply the initial area by the growth factor raised to the power of the number of months. Mathematically, this can be represented as:
[tex]\[
\text{final area} = \text{initial area} \times (\text{growth rate})^{\text{time period}}
\][/tex]
5. Perform the Calculation:
[tex]\[
\text{final area} = 11 \times (1.5)^6
\][/tex]
6. Result:
- Performing this calculation gives you approximately 125.3 square centimeters.
So, after 6 months, the moss will cover approximately 125.3 cm². Therefore, the correct answer is A. 125.3 cm².
1. Understand the Initial Conditions:
- The initial area of moss is 11 square centimeters.
2. Growth Factor per Month:
- Each month, the area of moss increases by a factor of 1.5.
3. Determine the Time Period:
- Paul will check the moss after 6 months.
4. Calculate the Final Area:
- To find out how much the moss grows, multiply the initial area by the growth factor raised to the power of the number of months. Mathematically, this can be represented as:
[tex]\[
\text{final area} = \text{initial area} \times (\text{growth rate})^{\text{time period}}
\][/tex]
5. Perform the Calculation:
[tex]\[
\text{final area} = 11 \times (1.5)^6
\][/tex]
6. Result:
- Performing this calculation gives you approximately 125.3 square centimeters.
So, after 6 months, the moss will cover approximately 125.3 cm². Therefore, the correct answer is A. 125.3 cm².
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