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Answer :
To find out how much area the moss will cover after 6 months, we need to consider the continuous growth of the moss each month. Here's how you can think about it step-by-step:
1. Initial Area: The moss initially covers an area of 11 square centimeters.
2. Growth Rate: Each month, the moss multiplies by one and a half times, which means the growth rate is 1.5.
3. Growth Period: We are interested in the growth over 6 months.
4. Calculation of Final Area: To find the area covered by the moss after 6 months, we will multiply the initial area by the growth rate raised to the power of the number of months. Mathematically, this is written as:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Months}}
\][/tex]
Plugging in the numbers:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
5. Result: After doing the calculation, the final area covered by the moss is approximately 125.3 square centimeters.
So, the closest option to this result is:
C. [tex]\(125.3 \, \text{cm}^2\)[/tex]
1. Initial Area: The moss initially covers an area of 11 square centimeters.
2. Growth Rate: Each month, the moss multiplies by one and a half times, which means the growth rate is 1.5.
3. Growth Period: We are interested in the growth over 6 months.
4. Calculation of Final Area: To find the area covered by the moss after 6 months, we will multiply the initial area by the growth rate raised to the power of the number of months. Mathematically, this is written as:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Months}}
\][/tex]
Plugging in the numbers:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
5. Result: After doing the calculation, the final area covered by the moss is approximately 125.3 square centimeters.
So, the closest option to this result is:
C. [tex]\(125.3 \, \text{cm}^2\)[/tex]
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