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Answer :
To solve the problem of determining how much area the moss will cover when Paul returns after 6 months, we can follow these steps:
1. Understand the Initial Conditions: We know that initially, the moss covers an area of 11 square centimeters.
2. Determine the Growth Rate: The moss grows by one and a half times its current size each month. This means that every month, the moss area is multiplied by 1.5.
3. Calculate Growth Over 6 Months:
- For the first month: Multiply the initial area by 1.5.
- For the second month: Again multiply the result from the previous month by 1.5.
- Continue this process for a total of 6 months.
To simplify, you can use the formula for exponential growth, where you multiply the initial area by the growth factor raised to the number of months.
Mathematically, this can be expressed as:
[tex]\[ \text{Final area} = \text{Initial area} \times (\text{Growth rate})^{\text{Number of months}} \][/tex]
[tex]\[ \text{Final area} = 11 \times (1.5)^6 \][/tex]
4. Calculate the Final Area: After calculating the power and performing the multiplication, you find that the approximate area covered by the moss after 6 months will be around 125.3 square centimeters.
Therefore, the correct answer is:
C. [tex]\(125.3 \, cm^2\)[/tex]
1. Understand the Initial Conditions: We know that initially, the moss covers an area of 11 square centimeters.
2. Determine the Growth Rate: The moss grows by one and a half times its current size each month. This means that every month, the moss area is multiplied by 1.5.
3. Calculate Growth Over 6 Months:
- For the first month: Multiply the initial area by 1.5.
- For the second month: Again multiply the result from the previous month by 1.5.
- Continue this process for a total of 6 months.
To simplify, you can use the formula for exponential growth, where you multiply the initial area by the growth factor raised to the number of months.
Mathematically, this can be expressed as:
[tex]\[ \text{Final area} = \text{Initial area} \times (\text{Growth rate})^{\text{Number of months}} \][/tex]
[tex]\[ \text{Final area} = 11 \times (1.5)^6 \][/tex]
4. Calculate the Final Area: After calculating the power and performing the multiplication, you find that the approximate area covered by the moss after 6 months will be around 125.3 square centimeters.
Therefore, the correct answer is:
C. [tex]\(125.3 \, cm^2\)[/tex]
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