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

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.