To solve this problem, let’s start by understanding how exponential growth works. The area covered by moss increases each month by multiplying by a growth rate. In this scenario, the initial area of the moss is 11 square centimeters, and the growth rate is 1.5 times per month over a span of 6 months.
The formula to find the final area after exponential growth is given by:
[tex]\[ \text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Number of Months}} \][/tex]
Plugging in the given values:
[tex]\[ \text{Initial Area} = 11 \, \text{cm}^2 \][/tex]
[tex]\[ \text{Growth Rate} = 1.5 \][/tex]
[tex]\[ \text{Number of Months} = 6 \][/tex]
So, the calculation is:
[tex]\[ \text{Final Area} = 11 \times (1.5)^6 \][/tex]
Following through with the calculation:
1. Calculate \( 1.5^6 \)
2. Multiply the result by 11
After performing the necessary calculations, we arrive at the final area as approximately \( 125.3 \, \text{cm}^2 \).
Thus, the correct answer is:
[tex]\[ \boxed{125.3 \, \text{cm}^2} \][/tex]
which corresponds to option:
C. [tex]\(125.3 \, \text{cm}^2\)[/tex]
