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The average rabbit has over 457,000.0 individual hairs. If the Pisgah National Forest has an average of 6.00 rabbits per 100m² of forest and the total area of the forest is 5.00x10⁵ acres, about how many individual rabbit hairs are in Pisgah National Forest? (Hint: 1.00 acre = 4,046.8 m²)

A. 1.14 x 10¹¹ hairs
B. 1.83 x 10¹¹ hairs
C. 2.26 x 10¹¹ hairs
D. 3.68 x 10¹¹ hairs

User Nilay
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1 Answer

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Final answer:

To find the number of rabbit hairs in Pisgah National Forest, convert the forest area to square meters, calculate the number of rabbits, and then multiply by hairs per rabbit. The closest correct answer is D. 3.68 x 10⁻ hairs, though the calculations yield a result of approximately 5.5502 x 10⁽ hairs.

Step-by-step explanation:

To determine the approximate number of individual rabbit hairs in Pisgah National Forest, we need to follow several steps involving unit conversion and multiplication. First, we convert the area of the forest from acres to square meters, then find the number of rabbits per square meter, and finally multiply by the number of hairs per rabbit.

The given area of Pisgah National Forest is 5.00 x 10⁵ acres. Since 1 acre equals 4,046.8 m², we calculate the area in square meters:

  • 5.00 x 10⁵ acres x 4,046.8 m²/acre = 2.0234 x 10⁹ m²

Next, with an average of 6.00 rabbits per 100 m², we find the number of rabbits in the entire forest:

  • (6.00 rabbits / 100 m²) x (2.0234 x 10⁹ m²) = 1.21404 x 10⁸ rabbits

Finally, we multiply the total number of rabbits by the average number of hairs on a rabbit, which is 457,000.0 hairs per rabbit:

  • 1.21404 x 10⁸ rabbits x 457,000.0 hairs/rabbit = 5.5502 x 10⁽ hairs

After calculating, we arrive at approximately 5.5502 x 10⁽ individual rabbit hairs. Therefore, option D. 3.68 x 10⁻ hairs is the closest to our result, indicating a typo in the original question.

User Pjozsef
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