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Answer :
To solve the problem of how much area the moss will cover in 6 months, we can use the concept of exponential growth. Here's a step-by-step guide to understanding the solution:
1. Identify the initial conditions:
- The initial area of moss is 11 square centimeters.
2. Determine the growth factor:
- The moss multiplies by one and a half times each month. This means the growth factor per month is 1.5.
3. Calculate the time period:
- Paul will return in 6 months to re-measure the area.
4. Apply exponential growth:
- To find out the area after 6 months, we use the formula for exponential growth:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Factor})^\text{Number of Months}
\][/tex]
- Plugging in the values:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
5. Perform the calculations:
- Calculate [tex]\( (1.5)^6 \)[/tex]. This results in approximately 11.390625.
- Multiply this by the initial area:
[tex]\[
11 \times 11.390625 = 125.296875
\][/tex]
6. Choose the closest answer:
- The calculated area is approximately 125.3 square centimeters.
Therefore, the area that the moss will cover when Paul returns is approximately [tex]\( \text{B. } 125.3 \, \text{cm}^2 \)[/tex].
1. Identify the initial conditions:
- The initial area of moss is 11 square centimeters.
2. Determine the growth factor:
- The moss multiplies by one and a half times each month. This means the growth factor per month is 1.5.
3. Calculate the time period:
- Paul will return in 6 months to re-measure the area.
4. Apply exponential growth:
- To find out the area after 6 months, we use the formula for exponential growth:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (\text{Growth Factor})^\text{Number of Months}
\][/tex]
- Plugging in the values:
[tex]\[
\text{Final Area} = 11 \times (1.5)^6
\][/tex]
5. Perform the calculations:
- Calculate [tex]\( (1.5)^6 \)[/tex]. This results in approximately 11.390625.
- Multiply this by the initial area:
[tex]\[
11 \times 11.390625 = 125.296875
\][/tex]
6. Choose the closest answer:
- The calculated area is approximately 125.3 square centimeters.
Therefore, the area that the moss will cover when Paul returns is approximately [tex]\( \text{B. } 125.3 \, \text{cm}^2 \)[/tex].
Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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