We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To determine how much area the moss will cover when Paul returns, we use the given information about the initial area and the growth rate.
1. Initial Area: The initial area covered by moss is 11 square centimeters.
2. Growth Rate: Every month, the area covered by moss multiplies by a factor of 1.5 (one and a half times).
3. Time Frame: Paul will come back in 6 months.
To find out how much area the moss will cover after 6 months, we'll use the formula for exponential growth:
[tex]\[ \text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Months}} \][/tex]
Substituting the given values into the formula:
[tex]\[ \text{Final Area} = 11 \times (1.5)^6 \][/tex]
Now, calculate:
1. Calculate [tex]\( 1.5^6 \)[/tex]:
- [tex]\( 1.5^6 = 11.390625 \)[/tex]
2. Multiply this result by the initial area:
- [tex]\( 11 \times 11.390625 = 125.296875 \)[/tex]
Therefore, the area covered by the moss after 6 months is approximately 125.3 square centimeters.
Thus, the correct answer is:
A. [tex]\( \quad 125.3 \, \text{cm}^2 \)[/tex]
1. Initial Area: The initial area covered by moss is 11 square centimeters.
2. Growth Rate: Every month, the area covered by moss multiplies by a factor of 1.5 (one and a half times).
3. Time Frame: Paul will come back in 6 months.
To find out how much area the moss will cover after 6 months, we'll use the formula for exponential growth:
[tex]\[ \text{Final Area} = \text{Initial Area} \times (\text{Growth Rate})^{\text{Months}} \][/tex]
Substituting the given values into the formula:
[tex]\[ \text{Final Area} = 11 \times (1.5)^6 \][/tex]
Now, calculate:
1. Calculate [tex]\( 1.5^6 \)[/tex]:
- [tex]\( 1.5^6 = 11.390625 \)[/tex]
2. Multiply this result by the initial area:
- [tex]\( 11 \times 11.390625 = 125.296875 \)[/tex]
Therefore, the area covered by the moss after 6 months is approximately 125.3 square centimeters.
Thus, the correct answer is:
A. [tex]\( \quad 125.3 \, \text{cm}^2 \)[/tex]
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