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Answer :
Certainly! Let's solve this step by step:
Paul initially measured an area of 11 square centimeters covered by moss. The moss grows by multiplying its area by 1.5 times every month. We need to find the area covered by moss after 6 months.
Let's break down the process:
1. Initial Area: [tex]\( 11 \)[/tex] square centimeters.
2. Growth Rate per Month: [tex]\( 1.5 \)[/tex].
3. Number of Months: [tex]\( 6 \)[/tex].
We can use the formula for exponential growth:
[tex]\[ \text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Number of Months}} \][/tex]
Plugging in the values:
[tex]\[ \text{Final Area} = 11 \times (1.5)^6 \][/tex]
Now we calculate [tex]\( 1.5^6 \)[/tex]:
- [tex]\( 1.5^6 = 11.390625 \)[/tex]
So, multiplying this by the initial area:
[tex]\[ \text{Final Area} = 11 \times 11.390625 \][/tex]
[tex]\[ \text{Final Area} \approx 125.3 \][/tex]
Therefore, after 6 months, the moss covers approximately [tex]\( 125.3 \)[/tex] square centimeters of the tree.
So, the correct answer is:
[tex]\[ \boxed{125.3 \text{ cm}^2} \][/tex]
Paul initially measured an area of 11 square centimeters covered by moss. The moss grows by multiplying its area by 1.5 times every month. We need to find the area covered by moss after 6 months.
Let's break down the process:
1. Initial Area: [tex]\( 11 \)[/tex] square centimeters.
2. Growth Rate per Month: [tex]\( 1.5 \)[/tex].
3. Number of Months: [tex]\( 6 \)[/tex].
We can use the formula for exponential growth:
[tex]\[ \text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Number of Months}} \][/tex]
Plugging in the values:
[tex]\[ \text{Final Area} = 11 \times (1.5)^6 \][/tex]
Now we calculate [tex]\( 1.5^6 \)[/tex]:
- [tex]\( 1.5^6 = 11.390625 \)[/tex]
So, multiplying this by the initial area:
[tex]\[ \text{Final Area} = 11 \times 11.390625 \][/tex]
[tex]\[ \text{Final Area} \approx 125.3 \][/tex]
Therefore, after 6 months, the moss covers approximately [tex]\( 125.3 \)[/tex] square centimeters of the tree.
So, the correct answer is:
[tex]\[ \boxed{125.3 \text{ cm}^2} \][/tex]
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