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

Answer :

We start with an initial moss area of [tex]$11 \text{ cm}^2$[/tex]. The area increases by a factor of [tex]$1.5$[/tex] each month. After [tex]$6$[/tex] months, the area can be calculated using the compound multiplication:

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

Calculating the multiplier gives:

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

Then, multiplying this result by [tex]$11$[/tex]:

[tex]$$
\text{Final area} \approx 11 \times 11.390625 \approx 125.3 \text{ cm}^2
$$[/tex]

Thus, when Paul returns, the moss will cover approximately [tex]$125.3 \text{ cm}^2$[/tex]. This corresponds to option D.

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