What does Activity mean in terms of radioactive decay?

[kraphysics]

What does "Activity" mean in terms of radioactive decay?

I came across this term "activity" in text regarding radioactive decay and half lives. It is defined as "number of nuclei in a sample that decay within a given time."
That definition if fine but then when presented in a graph life format, various activities were listed along with time in x axis, y-axis format. To me, it doesn't make any sense because it's saying the activity at 0min is 8, activity at 10 min is 5, activity at 20 min is 3.17 etc.. I don't understand what this means.
Does it mean that for ex. by 10 min, 3 nuclei have decayed? if so, why would 4 nuclei have decayed by half life? I thought the decay rate could fluctuate and it doesn't have to follow a trend except by a certain half- live, number of nuclei left would be half of original?
Wouldn't this be less confusing to list "number of nuclei left vs time"?

 

[eXorikos]

The activity always diminishes. It is defined at decay constant times the number of nuclei of that type. The number of nuclei is not a fixed number. When a number of nuclei decay, there are less nuclei that can decay. In formula it looks like this:

$$N = N_0 \exp{-\lambda t}$$
$$\lambda N = \lambda N_0 \exp{-\lambda t}$$
$$A = A_0 \exp{-\lambda t}$$
with N_0 the number of nuclei at t=0 and A_0 the activity at t=0

 

[jtbell]

Activity is a rate: number of decays per second, or decays per minute, or decays per hour, etc. Your example might mean:

t = 0 min, A = 8 decays/sec
t = 10 min, A = 5 decays/sec
t = 20 min, A = 3.17 decays/sec

Obviously, you can't have a fraction of a nucleus decaying, so the 3.17 must come from counting the number of decays during a longer period and then dividing by the time to get a rate. One possibility would be 19 decays / 6 sec which would give 3.17 decays/sec after rounding off to two decimal places.