This is a geometric progression:
Tn=a₁r^(n-1)
In this case:
Tn=a₁r^n
Because:
T₁ corresponds to 0 minutes ⇒T₁=3000(1/2)⁰=3000
T₂ corresponds to 1 minute ⇒ T²=3000(1/2)¹=1500 ...
Tn=375
a₁=3000
r=1/2
n=number of minutes
Therefore:
375=3000*(1/2)^n
375/3000=(1/2)^n
0.125=(1/2)^n
Ln 0.125=ln [(1/2)^n]
Ln 0.125=n Ln(1/2)
Ln 0.125=n [Ln1-Ln2]
Ln 0.125=n[0-Ln 2]
n=Ln 0.125 / (-Ln2)
n=3
answer: 3 minutes.