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Answer :
Certainly! Let's solve the question step-by-step:
Paul initially measures an area of 11 square centimeters covered by moss. The problem states that the moss grows by multiplying its area by one and a half times each month. We want to determine how much area the moss will cover after 6 months.
Here’s how to approach the problem:
1. Initial Situation: The area initially covered by moss is 11 square centimeters.
2. Growth Rate: Each month, the moss multiplies its area by 1.5. This means that the area grows to 1.5 times its size every month.
3. Time Frame: We are considering a total period of 6 months.
4. Calculation: To find the area after 6 months, we need to account for the growth of the moss over each of these months. This involves multiplying the initial area by the growth factor of 1.5, raised to the power of the number of months (which is 6 in this case).
The formula we use is:
[tex]\[
\text{Final area} = \text{Initial area} \times (\text{Growth factor})^{\text{Number of months}}
\][/tex]
5. Apply Values: Substituting the given values into the formula:
[tex]\[
\text{Final area} = 11 \times (1.5)^6
\][/tex]
6. Result: Calculating this gives us approximately 125.3 square centimeters.
Thus, after 6 months, Paul can expect the moss to cover approximately 125.3 square centimeters. Therefore, the correct answer is option B: [tex]\( 125.3 \, cm^2 \)[/tex].
Paul initially measures an area of 11 square centimeters covered by moss. The problem states that the moss grows by multiplying its area by one and a half times each month. We want to determine how much area the moss will cover after 6 months.
Here’s how to approach the problem:
1. Initial Situation: The area initially covered by moss is 11 square centimeters.
2. Growth Rate: Each month, the moss multiplies its area by 1.5. This means that the area grows to 1.5 times its size every month.
3. Time Frame: We are considering a total period of 6 months.
4. Calculation: To find the area after 6 months, we need to account for the growth of the moss over each of these months. This involves multiplying the initial area by the growth factor of 1.5, raised to the power of the number of months (which is 6 in this case).
The formula we use is:
[tex]\[
\text{Final area} = \text{Initial area} \times (\text{Growth factor})^{\text{Number of months}}
\][/tex]
5. Apply Values: Substituting the given values into the formula:
[tex]\[
\text{Final area} = 11 \times (1.5)^6
\][/tex]
6. Result: Calculating this gives us approximately 125.3 square centimeters.
Thus, after 6 months, Paul can expect the moss to cover approximately 125.3 square centimeters. Therefore, the correct answer is option B: [tex]\( 125.3 \, cm^2 \)[/tex].
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