What is the half-life?

Question

It is known that the mass, m(t), of a radio-active substance decreases as it decays, and that the equation governing this is

m′(t)=−0.015m(t) where t is in years. What is the half-life?

 

I couldn't figure this one out, any help would be appreciated! Writing out the steps would also help me understand this problem better! 

Answer 1

There's a formula for half-life, given either the expected whole life (not what you have here) or the decay constant (the 0.015 you do have here). You can check the textbook for the background on the formula, but for this problem

 

half-life = ln 2 / decay constant = 0.693 / 0.015

 

So if we assume the decay constant is using consistent time units (I trust you for that), the half-life is just over 46 years. 46.2.

 

Cheers!