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

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

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

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

Answer :

To solve the problem, we start with the initial area of moss, which is
[tex]$$11 \text{ cm}^2.$$[/tex]

The moss grows by multiplying its area by [tex]$1.5$[/tex] every month. After [tex]$6$[/tex] months, the area will be

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

Evaluating [tex]$(1.5)^6$[/tex] gives approximately

[tex]$$ (1.5)^6 \approx 11.39. $$[/tex]

Now, multiply the initial area by this growth factor:

[tex]$$ \text{Final area} \approx 11 \times 11.39 \approx 125.3 \text{ cm}^2. $$[/tex]

Thus, the moss will cover approximately [tex]$125.3 \text{ cm}^2$[/tex] after 6 months.

The correct answer is B.

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