In order to determine a half-life directly from obervational data, the radioactive substance must decay rapidly enough that one can actually measure a change. Not surprisingly, the earliest radioactive substances studied were ones that decayed fairly rapidly. The data in the following table are from a paper published by Meyer and von Schweidler in 1905. Their numbers are not amounts but rather measurements of relative activity. Since the rate of radioactive emission is proportional to the amount present, one can measure amounts (relative to the starting amount) by observing instead the emission rates (relative to the starting rate).

Time (days)	Relative Activity
0.2	35.0
2.2	25.0
4.0	22.1
5.0	17.9
6.0	16.8
8.0	13.7
11.0	12.4
12.0	10.3
15.0	7.5
18.0	4.9
26.0	4.0
33.0	2.4
39.0	1.4
45.0	1.1
Source: S. Meyer and E. von Schweidler, Sitzungberichte der Akademie der Wissenschaften zu Wien, Mathematisch-Naturwissenschaftliche Classe, p. 1202 (Table 5), 1905.

In the worksheet, we model this data with an exponential function of the form:

y = y₀ 2 ^–t/T

This is just  y = y₀ b ^t  with  b = 2 ^–1/T. Notice that when  t = T,  y = y₀/2. In other words, T  is just the half-life, displayed conveniently as a parameter in the equation.