A certain type of bacteria doubles every 8 hours. A culture begins with 30 000. Without use of given equation, use the help 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

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