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Answer :
To solve the problem, we start with the following information:
- The initial area of moss is [tex]$11\ \text{cm}^2$[/tex].
- The area multiplies by [tex]$1.5$[/tex] each month.
- Paul measures the area again after [tex]$6$[/tex] months.
After [tex]$6$[/tex] months, the area is multiplied by the factor [tex]$1.5^6$[/tex]. We first compute this multiplier:
[tex]$$
\text{Multiplier} = 1.5^6 \approx 11.390625
$$[/tex]
Now, the area after [tex]$6$[/tex] months is calculated by multiplying the initial area by this factor:
[tex]$$
\text{Future Area} = 11 \times 11.390625 \approx 125.296875\ \text{cm}^2
$$[/tex]
Rounding to one decimal place gives approximately [tex]$125.3\ \text{cm}^2$[/tex].
Thus, the correct answer is:
[tex]$$\boxed{125.3\ \text{cm}^2}$$[/tex]
- The initial area of moss is [tex]$11\ \text{cm}^2$[/tex].
- The area multiplies by [tex]$1.5$[/tex] each month.
- Paul measures the area again after [tex]$6$[/tex] months.
After [tex]$6$[/tex] months, the area is multiplied by the factor [tex]$1.5^6$[/tex]. We first compute this multiplier:
[tex]$$
\text{Multiplier} = 1.5^6 \approx 11.390625
$$[/tex]
Now, the area after [tex]$6$[/tex] months is calculated by multiplying the initial area by this factor:
[tex]$$
\text{Future Area} = 11 \times 11.390625 \approx 125.296875\ \text{cm}^2
$$[/tex]
Rounding to one decimal place gives 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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