Every day, the number of fish in a pond doubles. if it takes 24 days to fill the entire pond with fish, how long does it take to fill half the pond?

Say initial population occupies 1/n of the pond.
 Given: (1/n)∗(2^24)=1
 Question: if (1/n)∗(2^x)=1/2 then x=?
 (1/n)∗(2^x)=1/2 --> (1/n)∗(2^x)∗(2)=1 --> (1/n)∗(2^(x+1))=1
 Since we know that
 (1/n)∗(2^24)=1
  then 
 2^(x+1)=2^24  --> x+1=24  --> x=23
 take 23 days to fill half the pond