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Answer :
To determine how much area the moss will cover after 6 months, we need to understand how the moss grows. Each month, the moss multiplies by one and a half times. This is an example of exponential growth.
1. Initial Area: Start with the initial area covered by the moss, which is [tex]\( 11 \, \text{cm}^2 \)[/tex].
2. Growth Rate: The moss multiplies by 1.5 times each month. This means in one month, the area is multiplied by 1.5, in two months by [tex]\( 1.5 \times 1.5 \)[/tex], and so on.
3. Formula for Exponential Growth:
[tex]\[
\text{Final area} = \text{Initial area} \times (\text{Growth rate})^{\text{Number of months}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Final area} = 11 \, \text{cm}^2 \times (1.5)^6
\][/tex]
4. Calculation:
- First, calculate [tex]\( 1.5^6 \)[/tex].
- Then multiply the result by 11 to find the final area in [tex]\( \text{cm}^2 \)[/tex].
After performing these calculations, we find that the moss will cover approximately [tex]\( 125.3 \, \text{cm}^2 \)[/tex] after 6 months.
Therefore, the correct answer is [tex]\( D. \, 125.3 \, \text{cm}^2 \)[/tex].
1. Initial Area: Start with the initial area covered by the moss, which is [tex]\( 11 \, \text{cm}^2 \)[/tex].
2. Growth Rate: The moss multiplies by 1.5 times each month. This means in one month, the area is multiplied by 1.5, in two months by [tex]\( 1.5 \times 1.5 \)[/tex], and so on.
3. Formula for Exponential Growth:
[tex]\[
\text{Final area} = \text{Initial area} \times (\text{Growth rate})^{\text{Number of months}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Final area} = 11 \, \text{cm}^2 \times (1.5)^6
\][/tex]
4. Calculation:
- First, calculate [tex]\( 1.5^6 \)[/tex].
- Then multiply the result by 11 to find the final area in [tex]\( \text{cm}^2 \)[/tex].
After performing these calculations, we find that the moss will cover approximately [tex]\( 125.3 \, \text{cm}^2 \)[/tex] after 6 months.
Therefore, the correct answer is [tex]\( D. \, 125.3 \, \text{cm}^2 \)[/tex].
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