Nuclear Decay with time (half-life,initial activity/ nuclei)

[Treeps]

Hi! I just keep having a hard time looking for the formula stating the relationship between half life, the initial number of unstable nuclei and the initial activity, can someone help me on that ?

To be more specific, here is a problem which can be solved using that formula:
"A substance has a half life of 100s, and starts with 10²⁰ unstable nuclei.Calculate the initial activity, and from this work out the time taken for all of the nuclei to decay if the activity did not decrease with time"

The only formulas I could find were:
A (final activity)= A₀*e^{-decay constant*time}
N (final number of nuclei)= N₀*e^{-decay constant*time}
But nothing clearing expressing the relationship between A₀ and N₀

 

[mfb]

Activity is the process of nuclei "going away" (decaying) - a derivative should help.

 

[Treeps]

Euh is it A₀=N₀*decay constant ?

 

[mfb]

Right.

 

[Treeps]

Ok, thanks for your help !