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Select the correct answer.

Paul is gathering data about moss growth in a local forest. He measured an area of 11 square centimeters on one particular tree and will come back in 6 months to measure the growth of the moss. If the area covered by moss multiplies by one and a half times each month, approximately how much area will the moss cover when Paul returns?

A. [tex]\( \quad 16.5 \, \text{cm}^2 \)[/tex]
B. [tex]\( \quad 125.3 \, \text{cm}^2 \)[/tex]
C. [tex]\( \quad 14.7 \, \text{cm}^2 \)[/tex]
D. [tex]\( \quad 99.1 \, \text{cm}^2 \)[/tex]

Answer :

To solve this problem and find the area the moss will cover after 6 months, you can follow these steps:

1. Start with the Initial Area: The initial area covered by moss is 11 square centimeters.

2. Determine the Growth Rate: The moss grows by one and a half times each month. This means the growth rate is 1.5 times the previous month's area.

3. Calculate the Growth Over 6 Months: To find the total coverage after 6 months, we multiply the area by the growth rate for each month. This means we raise the growth rate to the power of 6 (because there are 6 months of growth).

[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]

4. Perform the Calculation: Let's calculate the final area.

- [tex]\(1.5^6\)[/tex] equals approximately 11.390625.
- Multiply this by the initial area of 11 cm²:

[tex]\[
\text{Final Area} = 11 \times 11.390625 \approx 125.296875
\][/tex]

5. Choose the Closest Option: The closest option to 125.296875 from the given choices is 125.3 cm².

Therefore, the answer is B. [tex]\( \quad 125.3 \, \text{cm}^2 \)[/tex].

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