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

Answer :

To find out how much area the moss will cover when Paul returns after 6 months, we can follow these steps:

1. Initial Area: Start with the initial area covered by the moss, which is 11 square centimeters.

2. Growth Rate: The moss multiplies by one and a half times (which is the same as multiplying by 1.5) each month.

3. Number of Months: The time period is 6 months.

4. Calculation: To find the area covered after 6 months, we need to multiply the initial area by the growth factor raised to the power of the number of months. This means we calculate:

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

5. Result: Carrying out this calculation results in approximately 125.3 square centimeters.

Therefore, after 6 months, the moss will cover approximately 125.3 square centimeters. So, the correct answer is:

A. [tex]\( 125.3 \, \text{cm}^2 \)[/tex]

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