if a sample known to be about 10,740 years old has 400 carbon-14 atoms. how many atoms were in the sample when the organism dies

Carbon 14 has a half-life of about 5740 years

Since this is about 2  half-lives then 1/4 of the atoms would remain

meaning 1600 atoms were initially present , I assume that they mean the sample died 10,740 years ago

More accurately (T / 5740) = n = number of elapsed half-lives

(10740 / 5740)  = 1.87 half lives

(1/2)^1.87 = .273  of original amount left

400 / .273 = 1463  atoms originally present

when heated, the valance electrons increased their speed and transferred the heat from electron to electron.   i just took the test.