Scientists can determine the age of ancient objects by a method called radiocarbon dating. the bombardment of the upper atmosphere by cosmic rays converts nitrogen to 14c ,a radioactive isotope of carbon, with a half-life of about 5730 years. vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14c through food chains. when a plant or animal dies, it stops replacing its carbon and the amount of 14c begins to decrease through radioactive decay. therefore, the level of radioactivity must also decay exponentially. a parchment fragment was discovered that had about 13% as much 14c radioactivity as does plant material on earth today. estimate the age of the parchment.

select the correct answer.

a) t= 16,724 years
b) none of these
c) t= 17,150 years
d) t= 18,373 years
e) t= 16,866 years
f) t= 16,189 years

B

Explanation:

A detailed solution to the problem is shown in the image attached. You could study it. The half life, and percentage of C-14 compared to present living sample was given as 13% of that of a living sample.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.