Help with half-life decay equations

N = N₀e^(ln(2)*t/T) where t is time and T is half life

 

250 = 600e^(-ln(2)*20/T)

 

Divide by 600 and take logs

ln(25/60) = -ln((2)*20/T

 

Rearrange

T = -ln(2)*20/ln(25/60) years. ≈ 15.8 years

Another way:

Remaining = Original ( e^(-kt) )        where 'k' is  a decay constant

250 = 600 e^(-k * 20)        yields k = .0437734

1/2 of 600 is 300 so substitue to find 't1/2'

300 = 600 e^(-.0437734 *t) 

ln (300/600) = -.0437734 * t

t= 15.835 years                           (t1/2)

T=half-life

250 = 600.2^-(20/T), solve for T

T =~15.83488.......Years.