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Select the correct answer.

Paul is gathering data about moss growth in a local forest. He measured an area of [tex]11 \, \text{cm}^2[/tex] 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]14.7 \, \text{cm}^2[/tex]
B. [tex]16.5 \, \text{cm}^2[/tex]
C. [tex]99.1 \, \text{cm}^2[/tex]
D. [tex]125.3 \, \text{cm}^2[/tex]

Answer :

To solve the problem, we start by noting that the initial area is

[tex]$$
11 \text{ cm}^2.
$$[/tex]

The moss grows by a factor of 1.5 each month, and Paul will return in 6 months. Therefore, after 6 months, the area covered by the moss is given by

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

Calculating the growth factor:

[tex]$$
(1.5)^6 \approx 11.390625.
$$[/tex]

Now, multiplying the initial area by this growth factor, we get:

[tex]$$
11 \times 11.390625 \approx 125.296875 \text{ cm}^2.
$$[/tex]

Rounding to one decimal place, the area is approximately

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

Thus, the correct answer is:

[tex]$$
\boxed{125.3 \text{ cm}^2 \text{ (Option D)}.}
$$[/tex]

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