A bacteria culture has an initial population of 200 bacteria at 9:00 AM and, in the presence of sufficient nutrients, the population doubles every 25 minutes. At approximately what time will there be 100,000 bacteria?

Answer 1

number = 200(2)^(t/25), where t is in minutes, so ...

200(2^(t/25) ) = 100000
2^(t/25) = 500
take logs of both sides and use your log rules:
t/25 log2 = log 500
t/25 = log500/log2
t = 25(log500/log2)
= .... minutes

Answer 2

The course I'm taking does not use log..

Answer 3

In that case you could proceed like this
after 25 minutes --- 400
after 50 minutes --- 800
after 75 minutes --- 1600
after 100 minutes --- 3200
after 125 minutes --- 6400
after 150 minutes --- 12800
after 175 minutes --- 25600
after 200 minutes --- 51200
after 225 minutes --- 102400 , we needed 100,000, so just short of 225 minutes would do it

my answer using logs would be 224.14 minutes

so 225 minutes would be the closest you could get not using logs,
and 225 minutes after 9:00 am would be 12:45 (I added 3 hrs and 45 minutes)