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Answer :
To find out how much area the moss will cover after 6 months, we need to consider the growth pattern. We know that the moss's area multiplies by 1.5 times each month. Let's go through the steps to calculate the area after 6 months.
1. Initial Area: Start with an area of 11 square centimeters.
2. Growth Factor: Each month, the area of moss multiplies by 1.5.
3. Number of Months: We're interested in what happens after 6 months.
4. Calculation:
- After 1 month, the area will be:
[tex]\[
11 \times 1.5
\][/tex]
- After 2 months:
[tex]\[
(11 \times 1.5) \times 1.5 = 11 \times 1.5^2
\][/tex]
- Continuing this process for 6 months:
[tex]\[
\text{Area after 6 months} = 11 \times 1.5^6
\][/tex]
5. Result: When calculated, the area after 6 months is approximately 125.3 square centimeters.
So, the moss will cover an area of approximately 125.3 square centimeters after 6 months. Therefore, the correct answer is A. [tex]$125.3\ cm^2$[/tex].
1. Initial Area: Start with an area of 11 square centimeters.
2. Growth Factor: Each month, the area of moss multiplies by 1.5.
3. Number of Months: We're interested in what happens after 6 months.
4. Calculation:
- After 1 month, the area will be:
[tex]\[
11 \times 1.5
\][/tex]
- After 2 months:
[tex]\[
(11 \times 1.5) \times 1.5 = 11 \times 1.5^2
\][/tex]
- Continuing this process for 6 months:
[tex]\[
\text{Area after 6 months} = 11 \times 1.5^6
\][/tex]
5. Result: When calculated, the area after 6 months is approximately 125.3 square centimeters.
So, the moss will cover an area of approximately 125.3 square centimeters after 6 months. Therefore, the correct answer is A. [tex]$125.3\ cm^2$[/tex].
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