Question 301820
N(t) = 310 000 (1/2) ^t

5000 = N(t)

5000 = 310 000 (1/2) ^t

5000/31000 = (1/2)^t

1/62 = (1/2)^t

Using log: 

t = [ lg(1/62) ] / [ lg (1/2) ] 
  = 5.95 years