High School

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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 return 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 \, cm^2 [/tex]
B. [tex] 99.1 \, cm^2 [/tex]
C. [tex] 16.5 \, cm^2 [/tex]
D. [tex] 125.3 \, cm^2 [/tex]

Answer :

We start with an initial area of moss of [tex]$11 \text{ cm}^2$[/tex]. The moss grows such that its area multiplies by [tex]$1.5$[/tex] each month. After [tex]$6$[/tex] months, the total multiplication factor is

[tex]$$
1.5^6.
$$[/tex]

Evaluating the exponent, we get

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

Now, multiplying the initial area by this factor gives us the final area:

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

Rounded to one decimal place, this 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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