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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. 127 cm[tex]\(^2\)[/tex]
B. [tex]$98.1 \, \text{cm}^2$[/tex]
C. None of these
D. [tex]$16.5 \, \text{cm}^2$[/tex]

Answer :

To determine how much area the moss will cover when Paul returns after 6 months, we need to consider how the growth of the moss compounds each month.

Here's a step-by-step breakdown:

1. Initial Area: Paul initially measured an area of moss that is 11 square centimeters.

2. Growth Factor: The moss area multiplies by one and a half times each month. This means each month the area will be [tex]\(1.5\)[/tex] times the previous month's area.

3. Number of Months: Paul will return in 6 months.

4. Calculating Growth Over 6 Months:
- We will use a formula for exponential growth, which is:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Factor})^\text{Number of Months}
\][/tex]
- Plug in the values:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]

5. Result: After performing the calculations, the moss will approximately cover an area of [tex]\(125.296875\)[/tex] square centimeters when Paul returns.

Therefore, the closest option to this value is A. 127.

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