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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 will the moss cover when Paul returns?

A. [tex]14.7 \, \text{cm}^2[/tex]

B. [tex]16.5 \, \text{cm}^2[/tex]

C. [tex]125.3 \, \text{cm}^2[/tex]

D. [tex]99.1 \, \text{cm}^2[/tex]

Answer :

We start with an initial moss-covered area of
[tex]$$
A_0 = 11\text{ cm}^2.
$$[/tex]

Since the area multiplies by [tex]$1.5$[/tex] each month, after [tex]$6$[/tex] months the area will be multiplied by
[tex]$$
1.5^6.
$$[/tex]

Thus, the final area [tex]$A$[/tex] is given by:
[tex]$$
A = 11 \times 1.5^6.
$$[/tex]

Evaluating [tex]$1.5^6$[/tex], we find that it is approximately [tex]$11.390625$[/tex]. Now, multiplying:
[tex]$$
A \approx 11 \times 11.390625 \approx 125.296875\text{ cm}^2.
$$[/tex]

Rounding to one decimal place, the area is approximately [tex]$125.3\text{ cm}^2$[/tex].

Therefore, the correct answer is option C.

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