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Answer :
To solve the problem of determining how much area the moss will cover when Paul returns, we need to consider the exponential growth of the moss over the 6-month period.
1. Understand the Initial Conditions:
- Paul starts with an area of 11 square centimeters of moss on the tree.
2. Determine the Growth Rate:
- The moss multiplies by one and a half times each month. This means the growth factor is 1.5.
3. Calculate Growth Over 6 Months:
- Since the moss grows by a factor of 1.5 each month, we need to raise the growth factor to the power of the number of months to find the total growth over that period. In this case, 6 months.
4. Calculate the Final Area:
- We start with an initial area of 11 cm². To find the area after 6 months, we multiply the initial area by the growth factor raised to the power of 6:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
5. Compute the Result:
- When you perform this calculation, you find that the moss will cover approximately 125.3 cm² after 6 months.
Based on the calculations, the correct answer is:
D. 125.3 cm².
1. Understand the Initial Conditions:
- Paul starts with an area of 11 square centimeters of moss on the tree.
2. Determine the Growth Rate:
- The moss multiplies by one and a half times each month. This means the growth factor is 1.5.
3. Calculate Growth Over 6 Months:
- Since the moss grows by a factor of 1.5 each month, we need to raise the growth factor to the power of the number of months to find the total growth over that period. In this case, 6 months.
4. Calculate the Final Area:
- We start with an initial area of 11 cm². To find the area after 6 months, we multiply the initial area by the growth factor raised to the power of 6:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
5. Compute the Result:
- When you perform this calculation, you find that the moss will cover approximately 125.3 cm² after 6 months.
Based on the calculations, the correct answer is:
D. 125.3 cm².
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