There are other isotopes of cerium which are radioactive. Different isotopes of cerium have different half-lives.
The half-life of an isotope can be found by studying how the number of atoms
changes over time.
Figure 7 shows how the number of atoms of cerium-148 in a 120 g sample changes
over time.
1. Determine the ratio of the number of cerium atoms in the sample when it was 100 seconds old compared with when the sample was 350 seconds old. Use data from Figure 7.
2. Determine the activity of the sample of cerium when the sample was 20 seconds old. Use Figure 7.

hypothesising or postulating

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.