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Answer :
To find out how much area the moss will cover when Paul returns after 6 months, we need to consider the initial area of the moss and how much it grows over time. Here's a step-by-step breakdown of the process:
1. Initial Area: Start with an area of 11 square centimeters.
2. Growth Rate: The moss multiplies its covered area by one and a half times (1.5 times) each month.
3. Time Period: Paul will be returning in 6 months.
4. Calculate Growth: To find the total area covered by the moss after 6 months, we need to use the formula for exponential growth. This can be expressed mathematically as:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Number of Months}}
\][/tex]
5. Perform the Calculation:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
6. Result: When you calculate [tex]\(11 \times (1.5)^6\)[/tex], you get approximately 125.3 square centimeters.
Therefore, the area that the moss will cover when Paul returns is approximately [tex]\(125.3 \, \text{cm}^2\)[/tex].
Thus, the correct answer is:
A. [tex]\(125.3 \, \text{cm}^2\)[/tex]
1. Initial Area: Start with an area of 11 square centimeters.
2. Growth Rate: The moss multiplies its covered area by one and a half times (1.5 times) each month.
3. Time Period: Paul will be returning in 6 months.
4. Calculate Growth: To find the total area covered by the moss after 6 months, we need to use the formula for exponential growth. This can be expressed mathematically as:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Number of Months}}
\][/tex]
5. Perform the Calculation:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
6. Result: When you calculate [tex]\(11 \times (1.5)^6\)[/tex], you get approximately 125.3 square centimeters.
Therefore, the area that the moss will cover when Paul returns is approximately [tex]\(125.3 \, \text{cm}^2\)[/tex].
Thus, the correct answer is:
A. [tex]\(125.3 \, \text{cm}^2\)[/tex]
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