Is There a Shortcut for Solving Half-Life Decay Equations?

[Trustworthy]

A 100 mg sample of magnesium-27 decays by 7% of its previous mass every minute. Determine its half-life and start the half-life decay equation.

The textbook that I got this from (Nelson Physics 11) tells me the answer, but uses a long and annoying process to find it: creating a table at different points in time and then graphing. I am just wondering if there is an equation or some sort of trick to this type of question? It would save me a lot of time and trouble, thank you in advance.

 

[ChrisVer]

It's a series.. it tells you that at each minute it loses 7% of what it had before... So it's better to use a table and see it...

 

[Orodruin]

Yes, it is very possible to derive a general expression for the amount left after a given time. If the sample loses 7% of its mass every minute, what is the ratio of mass left to original mass after 1 minute? What is the ratio after two minutes? Three minutes? Do you see a pattern? In that case, what should be the mass left after a time T?

 

[arivero]

To honour the "Compound" in the title of the post... Can someone point to the general formula for a decay chain, with elements having different half-lifes?

 

[mfb]

The right formula depends on what you want to know, but it is possible to get everything with the right integral for the considered problem.

 

[Meir Achuz]

The question seems too simple.
$\exp(-t/\tau)=0.93$, so $\tau=-1/\ln(.93)$ in minutes.