Final answer:
The student's question is answered by explaining the concept of half-life in the context of Carbon-14 decay and by demonstrating how to compare different customary units of weight by converting tons to pounds to find how many polar bears would equal the weight of a humpback whale.
Step-by-step explanation:
The subject matter of the student's question pertains to Mathematics, specifically involving the concept of half-life in radioactive decay, which applies to the decomposition of Carbon-14 in an organism after death. Additionally, the question also includes the comparison of weights using customary units. Here's an explanation of the mentioned problems:
Problem 1: Understanding Half-life
When a hippopotamus passes away with a total of 25 grams of Carbon-14, after 5730 years, which is the half-life of Carbon-14, only half of the original amount remains. Therefore, you would have 12.5 grams of Carbon-14 left. The half-life is the time required for half of the radioactive isotope present to decay.
Problem 2: Calculating Multiple Half-lives
After three half-lives have passed, you would apply the half-life decay process three times to the original 25 grams of Carbon-14. After one half-life, as stated before, you have 12.5 grams; after the second, you would have half of 12.5 grams, which is 6.25 grams; and after the third half-life, you would have half of 6.25 grams, or 3.125 grams of Carbon-14 remaining.
Comparing Weights of Marine Animals and Bears
To compare the weights, you must convert tons to pounds (as there are 2000 pounds in a ton) then divide the weight of the whale by the weight of a polar bear. A humpback whale weighs 40 tons, which is equivalent to 80,000 pounds (40 tons x 2000 pounds/ton), and thus, it would take approximately 80 polar bears of 1000 pounds each to equal the weight of one humpback whale.