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Answer :
Sure, let's break down the steps to understand how to determine the area covered by moss after 6 months, given that the area increases by 1.5 times each month.
1. Initial Information:
- Initial area of moss = 11 square centimeters
- Monthly growth rate = 1.5 (or 150%)
- Time period = 6 months
2. Understanding Growth:
- Each month, the area grows by multiplying the current area by 1.5.
- Mathematically, for each month, the new area = previous area × 1.5.
3. Formula for Exponential Growth:
- The area after [tex]\( n \)[/tex] months can be found using the formula:
[tex]\[
\text{Final area} = \text{Initial area} \times (\text{growth rate})^n
\][/tex]
- Here, the initial area is 11 sq cm, the growth rate is 1.5, and [tex]\( n \)[/tex] is 6 months.
4. Calculation:
- Plug in the values to the formula:
[tex]\[
\text{Final area} = 11 \times (1.5)^6
\][/tex]
- To compute [tex]\( (1.5)^6 \)[/tex]:
[tex]\[
(1.5)^6 = 11.390625
\][/tex]
- Multiply this by the initial area (11 sq cm):
[tex]\[
\text{Final area} = 11 \times 11.390625 = 125.296875 \text{ square centimeters}
\][/tex]
5. Conclusion:
- Rounding 125.296875 to one decimal place, we get approximately 125.3 square centimeters.
Therefore, the correct answer is:
C. [tex]\( 125.3 \, \text{cm}^2 \)[/tex].
1. Initial Information:
- Initial area of moss = 11 square centimeters
- Monthly growth rate = 1.5 (or 150%)
- Time period = 6 months
2. Understanding Growth:
- Each month, the area grows by multiplying the current area by 1.5.
- Mathematically, for each month, the new area = previous area × 1.5.
3. Formula for Exponential Growth:
- The area after [tex]\( n \)[/tex] months can be found using the formula:
[tex]\[
\text{Final area} = \text{Initial area} \times (\text{growth rate})^n
\][/tex]
- Here, the initial area is 11 sq cm, the growth rate is 1.5, and [tex]\( n \)[/tex] is 6 months.
4. Calculation:
- Plug in the values to the formula:
[tex]\[
\text{Final area} = 11 \times (1.5)^6
\][/tex]
- To compute [tex]\( (1.5)^6 \)[/tex]:
[tex]\[
(1.5)^6 = 11.390625
\][/tex]
- Multiply this by the initial area (11 sq cm):
[tex]\[
\text{Final area} = 11 \times 11.390625 = 125.296875 \text{ square centimeters}
\][/tex]
5. Conclusion:
- Rounding 125.296875 to one decimal place, we get approximately 125.3 square centimeters.
Therefore, the correct answer is:
C. [tex]\( 125.3 \, \text{cm}^2 \)[/tex].
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