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Answer :
To solve this problem, we need to find out how much area the moss will cover in 6 months if it grows by one and a half times each month.
1. Initial Area: The initial area covered by moss is 11 square centimeters.
2. Growth Factor: Each month, the area covered by moss multiplies by one and a half times, which can be expressed as a growth factor of 1.5 per month.
3. Time Period: We are looking at a time period of 6 months.
4. Formula for Growth: The formula for exponential growth is:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Factor})^{\text{Number of Months}}
\][/tex]
5. Plug in the Values:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
6. Calculate [tex]\( (1.5)^6 \)[/tex]:
[tex]\[
(1.5)^6 \approx 11.390625
\][/tex]
7. Calculate the Final Area:
[tex]\[
\text{Final Area} = 11 \times 11.390625 = 125.296875
\][/tex]
After rounding, the approximate area is [tex]\( 125.3 \, \text{cm}^2 \)[/tex]. Therefore, the correct answer is:
D. [tex]\( 125.3 \, \text{cm}^2 \)[/tex]
1. Initial Area: The initial area covered by moss is 11 square centimeters.
2. Growth Factor: Each month, the area covered by moss multiplies by one and a half times, which can be expressed as a growth factor of 1.5 per month.
3. Time Period: We are looking at a time period of 6 months.
4. Formula for Growth: The formula for exponential growth is:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Factor})^{\text{Number of Months}}
\][/tex]
5. Plug in the Values:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
6. Calculate [tex]\( (1.5)^6 \)[/tex]:
[tex]\[
(1.5)^6 \approx 11.390625
\][/tex]
7. Calculate the Final Area:
[tex]\[
\text{Final Area} = 11 \times 11.390625 = 125.296875
\][/tex]
After rounding, the approximate area is [tex]\( 125.3 \, \text{cm}^2 \)[/tex]. Therefore, the correct answer is:
D. [tex]\( 125.3 \, \text{cm}^2 \)[/tex]
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