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Answer :
To find the area that the moss will cover after 6 months, we need to consider how the moss grows over time. The key information here is that the moss area multiplies by one and a half times each month, starting with an initial area of 11 square centimeters.
Here's a step-by-step breakdown:
1. Initial Area: The moss initially covers an area of 11 square centimeters.
2. Growth Rate: Each month, the area covered by the moss is multiplied by 1.5 times (or 150%).
3. Time Period: We are interested in the growth after 6 months.
4. Calculating Final Area: To find the final area covered by the moss, we use the concept of exponential growth. This means we repeatedly multiply the initial area by the growth rate for each of the 6 months.
The formula for the final area after 6 months is:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Months}}
\][/tex]
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
After calculating, the final area that the moss will cover is approximately 125.3 square centimeters.
Based on this calculation, the closest answer to the amount of area the moss will cover in 6 months is:
B. 125.3 cm²
Here's a step-by-step breakdown:
1. Initial Area: The moss initially covers an area of 11 square centimeters.
2. Growth Rate: Each month, the area covered by the moss is multiplied by 1.5 times (or 150%).
3. Time Period: We are interested in the growth after 6 months.
4. Calculating Final Area: To find the final area covered by the moss, we use the concept of exponential growth. This means we repeatedly multiply the initial area by the growth rate for each of the 6 months.
The formula for the final area after 6 months is:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Months}}
\][/tex]
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
After calculating, the final area that the moss will cover is approximately 125.3 square centimeters.
Based on this calculation, the closest answer to the amount of area the moss will cover in 6 months is:
B. 125.3 cm²
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