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Answer :
Sure, let's solve this question step by step.
Paul starts with an initial moss area of 11 square centimeters. We need to determine the area covered by moss after 6 months if the moss area multiplies by one and a half times each month.
Here's how we can calculate it:
1. Identify the initial area:
- Initial area = [tex]\( 11 \, \text{cm}^2 \)[/tex]
2. Identify the growth rate per month:
- Growth rate per month = 1.5 times
3. Calculate the area covered after each month:
- Formula to calculate area after each month:
[tex]\[
\text{Final area} = \text{Initial area} \times (\text{Growth rate})^{\text{Number of months}}
\][/tex]
4. Substitute the values into the formula:
[tex]\[
\text{Final area} = 11 \times (1.5)^6
\][/tex]
5. Evaluate the exponent:
- [tex]\( (1.5)^6 \approx 11.390625 \)[/tex]
6. Multiply the initial area by the result:
- [tex]\( 11 \times 11.390625 \approx 125.3 \, \text{cm}^2 \)[/tex]
Therefore, the area of the moss after 6 months will be approximately [tex]\( 125.3 \, \text{cm}^2 \)[/tex].
So, the correct answer is:
B. [tex]\( 125.3 \, \text{cm}^2 \)[/tex]
Paul starts with an initial moss area of 11 square centimeters. We need to determine the area covered by moss after 6 months if the moss area multiplies by one and a half times each month.
Here's how we can calculate it:
1. Identify the initial area:
- Initial area = [tex]\( 11 \, \text{cm}^2 \)[/tex]
2. Identify the growth rate per month:
- Growth rate per month = 1.5 times
3. Calculate the area covered after each month:
- Formula to calculate area after each month:
[tex]\[
\text{Final area} = \text{Initial area} \times (\text{Growth rate})^{\text{Number of months}}
\][/tex]
4. Substitute the values into the formula:
[tex]\[
\text{Final area} = 11 \times (1.5)^6
\][/tex]
5. Evaluate the exponent:
- [tex]\( (1.5)^6 \approx 11.390625 \)[/tex]
6. Multiply the initial area by the result:
- [tex]\( 11 \times 11.390625 \approx 125.3 \, \text{cm}^2 \)[/tex]
Therefore, the area of the moss after 6 months will be approximately [tex]\( 125.3 \, \text{cm}^2 \)[/tex].
So, the correct answer is:
B. [tex]\( 125.3 \, \text{cm}^2 \)[/tex]
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