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Answer :
To solve this problem, we need to determine the area that moss will cover after 5 months, given its growth rate.
1. Initial Area: The initial area covered by moss is 11 square centimeters.
2. Growth Rate: The moss grows at a rate of one and a half times its area each month. This means that every month the area becomes 1.5 times larger than the previous month.
3. Time Frame: We are considering a period of 5 months.
4. Exponential Growth Calculation: To find the area covered by the moss after 5 months, we use the exponential growth formula:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Rate}^{\text{Number of Months}})
\][/tex]
5. Calculation:
- Substitute the values into the formula:
[tex]\[
\text{Final Area} = 11 \times (1.5^5)
\][/tex]
- The calculation yields approximately 83.53 square centimeters.
Thus, after 5 months, the moss will cover approximately 83.53 cm².
None of the options provided in the question exactly match this calculation. Please double-check the options to ensure they are correct or consider the calculation as accurate given the growth conditions.
1. Initial Area: The initial area covered by moss is 11 square centimeters.
2. Growth Rate: The moss grows at a rate of one and a half times its area each month. This means that every month the area becomes 1.5 times larger than the previous month.
3. Time Frame: We are considering a period of 5 months.
4. Exponential Growth Calculation: To find the area covered by the moss after 5 months, we use the exponential growth formula:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Rate}^{\text{Number of Months}})
\][/tex]
5. Calculation:
- Substitute the values into the formula:
[tex]\[
\text{Final Area} = 11 \times (1.5^5)
\][/tex]
- The calculation yields approximately 83.53 square centimeters.
Thus, after 5 months, the moss will cover approximately 83.53 cm².
None of the options provided in the question exactly match this calculation. Please double-check the options to ensure they are correct or consider the calculation as accurate given the growth conditions.
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