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Answer :
To solve the problem, we start with the following information:
- The initial area covered by moss is [tex]$$11 \text{ cm}^2.$$[/tex]
- The area multiplies by [tex]$$1.5$$[/tex] every month.
- Paul will check back in [tex]$$6$$[/tex] months.
The growth each month is multiplicative, meaning the area after [tex]$$n$$[/tex] months is given by
[tex]$$
\text{Final Area} = \text{Initial Area} \times (1.5)^n.
$$[/tex]
Here, [tex]$$n = 6$$[/tex] months, so the calculation is
[tex]$$
\text{Final Area} = 11 \times (1.5)^6.
$$[/tex]
Calculating [tex]$$1.5^6$$[/tex] gives approximately [tex]$$11.390625$$[/tex]. Multiplying by the initial area:
[tex]$$
\text{Final Area} \approx 11 \times 11.390625 \approx 125.296875 \text{ cm}^2.
$$[/tex]
Rounding to one decimal place, the area is approximately [tex]$$125.3 \text{ cm}^2.$$[/tex]
Thus, the correct answer is
[tex]$$\boxed{125.3 \text{ cm}^2}.$$[/tex]
- The initial area covered by moss is [tex]$$11 \text{ cm}^2.$$[/tex]
- The area multiplies by [tex]$$1.5$$[/tex] every month.
- Paul will check back in [tex]$$6$$[/tex] months.
The growth each month is multiplicative, meaning the area after [tex]$$n$$[/tex] months is given by
[tex]$$
\text{Final Area} = \text{Initial Area} \times (1.5)^n.
$$[/tex]
Here, [tex]$$n = 6$$[/tex] months, so the calculation is
[tex]$$
\text{Final Area} = 11 \times (1.5)^6.
$$[/tex]
Calculating [tex]$$1.5^6$$[/tex] gives approximately [tex]$$11.390625$$[/tex]. Multiplying by the initial area:
[tex]$$
\text{Final Area} \approx 11 \times 11.390625 \approx 125.296875 \text{ cm}^2.
$$[/tex]
Rounding to one decimal place, the area is approximately [tex]$$125.3 \text{ cm}^2.$$[/tex]
Thus, the correct answer is
[tex]$$\boxed{125.3 \text{ cm}^2}.$$[/tex]
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