Acertain type of bacteria doubles every 8 hours. a culture begins with 30 000. without use of given equation, use the of your ability to set up a pattern to determine how many bacteria are there after a) 8 hours b) 16 hours c)d days

Not sure what you mean by "without use of given equation".
At time 0hrs, there is 30 000.
Since it doubles every 8hrs, at time 8hrs there is 60 000 or 30 000 x 2
In another 8hrs, it will double again, so at time 16hrs, it will be 120 000  or 30 000 x 2 x 2
In another 8hrs, double again, so at time 24hrs, it will be 240 000 or 30 000 x 2 x 2 x 2
This is also 30 000 x 8   as 2x2x2=8.  I'll come back to this later.

You add an extra x 2 for each 8 hrs. By the end of the 2nd day, it would be
30 000 x2 x2 x2    x2 x2 x2
This is also
30 000 x8  x8
Every day we add an extra x8
We use powers to specify this.
30 000 x 8^d
So after 4 days
30 000 x 8^4 = 30 000 x8 x8 x8 x8
Note that this is NOT the same as 30 000 x 8 x 4