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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 area will the moss cover when Paul returns?

A. [tex]125.3 \, \text{cm}^2[/tex]
B. [tex]16.5 \, \text{cm}^2[/tex]
C. [tex]99.1 \, \text{cm}^2[/tex]
D. [tex]14.7 \, \text{cm}^2[/tex]

Answer :

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

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

Calculating the multiplication factor:

[tex]$$1.5^6 = 11.390625.$$[/tex]

Thus, the final area after [tex]$6$[/tex] months is given by

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

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

Therefore, the correct answer is:

A. [tex]$\quad 125.3 cm^2$[/tex]

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