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Answer :
To solve this problem, we want to find out how much area the moss will cover after 6 months if it multiplies by one and a half times each month, starting from an initial area of 11 square centimeters.
Here's a step-by-step approach:
1. Understand the Growth Factor: The moss grows by one and a half times each month. This means every month the area multiplies by 1.5.
2. Initial Area: The starting area of moss on the tree is 11 square centimeters.
3. Calculate Growth Over 6 Months: Since the moss grows at a consistent rate each month, we will multiply the initial area by 1.5 for each month over a period of 6 months. In mathematical terms, this is expressed as multiplying the initial area by 1.5 raised to the power of 6. This can be written as:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
4. Calculate the Exponentiation: First, calculate the value of [tex]\(1.5^6\)[/tex].
5. Find the Final Area: Multiply 11 by the result from step 4 to get the final area of the moss.
Following the above steps, the area that the moss will cover after 6 months is approximately 125.3 square centimeters.
Therefore, the correct answer is:
A. [tex]\(125.3 \, \text{cm}^2\)[/tex]
Here's a step-by-step approach:
1. Understand the Growth Factor: The moss grows by one and a half times each month. This means every month the area multiplies by 1.5.
2. Initial Area: The starting area of moss on the tree is 11 square centimeters.
3. Calculate Growth Over 6 Months: Since the moss grows at a consistent rate each month, we will multiply the initial area by 1.5 for each month over a period of 6 months. In mathematical terms, this is expressed as multiplying the initial area by 1.5 raised to the power of 6. This can be written as:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
4. Calculate the Exponentiation: First, calculate the value of [tex]\(1.5^6\)[/tex].
5. Find the Final Area: Multiply 11 by the result from step 4 to get the final area of the moss.
Following the above steps, the area that the moss will cover after 6 months is approximately 125.3 square centimeters.
Therefore, the correct answer is:
A. [tex]\(125.3 \, \text{cm}^2\)[/tex]
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