At the beginning of an experiment, a scientist has 344 grams of radioactive goo. After 60 minutes, her sample has decayed to 43 grams. What is the half-life of the goo in minutes?

Answer 1

43=344e^60r

A=Pe^rt is a general formula for continuous decay, when r<0 r=rate of change

t= time, P = starting amount,A= ending amount,e=an irrational constant

43/344=e^60r

take natural logs of both sides

ln(43//344) = 60r

divide by 60

r = [ln(43/344)/60 = rate of change per minute = about -.03466= about negative 3.5% per minute

1/2 = e^rt

ln.5 = rt

t = (ln.5)/r = ln.5/(ln(43/344)/60 = 60(ln.5)/ln(43/344) = half life in minutes

t= about ln.5/-.03466 =20 minutes

t=0, goo = 344 grams

t=20 goo= 344/2= 172

t=40 goo= 172/2 = 86

t=60 goo= 86/2 = 43 grams after 3 half lives