explanation of conjugation experiment in bacteria
There are three variables being shown here: 


The amount of time samples were stored in the freezer to allow $^{32}$P decay (x-axis),
The length of time samples were allowed to grow in a nonradioactive environment before being frozen (points with different symbols), and
The rate of $\beta$-galactosidase production when cells were thawed and grown in the presence of the transcriptional inducer IPTG (y-axis).


Let's break those down a bit more:

The x-axis measures "fraction of $^{32}$P decay." In terms of the experimental protocol, this translates to "length of time left in the freezer." For the $^{32}$P-decay experiments, samples are stored in the freezer for various lengths of time, where metabolic processes, like DNA replication or enzyme production, are shut down or drastically slowed. Although metabolism has been shut down, $^{32}$P can still beta-decay into $^{31}$S (according to Wikipedia), which promotes the breakdown of any DNA containing (formerly) radioactive isotopes. The implication is that the longer you leave samples in the freezer, the more $^{32}$P will decay and the more formerly radioactive DNA will be degraded. So you can read the trend in the x-axis either as "increasing fraction of $^{32}$P decay", "increasing amount of time left in freezer," or "decreasing fraction of intact $z^+$ DNA." The different points corresponding to, say, "48 minutes past mating" correspond to samples that were frozen down 48 minutes past mating but kept in the freezer for different lengths of time.

The y-axis measures "percent survival of enzyme-forming capacity." I think that it's safe to interpret this as the rate of $\beta$-galactosidase production relative to the rate with no $^{32}$P-decay. In other words, if you plot $\beta$-galactosidase production over time (as in Figure 5) for different conditions, you'll measure a slope, the rate of enzyme production. If you normalize all these rates from different conditions by the rate when there was no radioactivity (and thus no degradation of $z^+$ DNA in the freezer), you'll get the values plotted on the y-axis.

The final interpretation of this plot is that the $\beta$-galactosidase production rate is sensitive to the loss of the introduced $z^+$ DNA when the loss occurs soon after mating, but if cells are allowed to grow enough to divide once or twice before DNA degradation, then the loss of the original conjugated $z^+$ DNA does not affect the $\beta$-galactosidase production rate. This data is consistent with the idea that the DNA form of a gene is constantly required for sustained $\beta$-galactosidase production, and after several rounds of division the $z^+$ DNA has been replicated and is no longer radioactive and prone to degradation.

There's a lot of data in this plot (ah, the elegance of 1960s molecular biology!) so it can take a while to digest. Hope this helps!