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Answer :
To determine how much area the moss will cover after 6 months, we need to understand that the moss’s growth is exponential. Here’s how we can calculate it step by step:
1. Initial Info: We know the initial area covered by moss is 11 square centimeters.
2. Growth Rate: The moss area grows by one and a half times each month. This means that each month, the area is multiplied by 1.5.
3. Time Period: We want to find out the area covered by the moss after 6 months.
4. Calculation: To find the area after 6 months, we need to repeatedly apply the growth rate for each month. This is an example of exponential growth.
- After 1 month, the area would be: [tex]\(11 \times 1.5\)[/tex].
- After 2 months, the area would grow again by a factor of 1.5: [tex]\(11 \times 1.5 \times 1.5\)[/tex].
- Continue this multiplication for each month up to 6 months.
We can write this calculation as:
[tex]\[
\text{Area after 6 months} = 11 \times (1.5)^6
\][/tex]
5. Result: When you do this calculation, you find that the area covered by the moss after 6 months is approximately 125.3 square centimeters.
Therefore, the correct answer is:
D. [tex]\(125.3 \, \text{cm}^2\)[/tex]
1. Initial Info: We know the initial area covered by moss is 11 square centimeters.
2. Growth Rate: The moss area grows by one and a half times each month. This means that each month, the area is multiplied by 1.5.
3. Time Period: We want to find out the area covered by the moss after 6 months.
4. Calculation: To find the area after 6 months, we need to repeatedly apply the growth rate for each month. This is an example of exponential growth.
- After 1 month, the area would be: [tex]\(11 \times 1.5\)[/tex].
- After 2 months, the area would grow again by a factor of 1.5: [tex]\(11 \times 1.5 \times 1.5\)[/tex].
- Continue this multiplication for each month up to 6 months.
We can write this calculation as:
[tex]\[
\text{Area after 6 months} = 11 \times (1.5)^6
\][/tex]
5. Result: When you do this calculation, you find that the area covered by the moss after 6 months is approximately 125.3 square centimeters.
Therefore, the correct answer is:
D. [tex]\(125.3 \, \text{cm}^2\)[/tex]
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