SOLUTION: A culture of 11 bacteria is started, and the number of bacteria will double every hour. In exactly how many hours, minutes, and seconds will there be 3,000,000,000 bacteria?

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Question 1018165: A culture of 11 bacteria is started, and the number of bacteria will double every hour. In exactly how many hours, minutes, and seconds will there be 3,000,000,000 bacteria?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +N+ = nuber of bacteria after +n+ hrs
+N+=+11%2A2%5En+
+N+=+3%2A10%5E9+
+3%2A10%5E9+=+11%2A2%5En+
+2%5En+=+%283%2F11%29%2A10%5E9+
Take the log base 10 of both sides
+n%2Alog%282%29+=+log%283%2F11%29+%2B+9+
+.30103n+=+log%28+.27273+%29+%2B+9+
+.30103n+=+-.56427+%2B+9+
+n+=+%28+1%2F.30103+%29%2A+8.43573+
+n+=+3.32193%2A8.43573+
+n+=+28.0229+
+.0229%2A60+=+1.374+
+.374%2A60+=+22.44+
In 28 hrs 1 min 22 sec there will
be +3%2A10%5E9+ bacteria
----------------------------
check:
+N+=+11%2A2%5En+
+3%2A10%5E9+=+11%2A2%5E28.0229+
+3%2A10%5E9+=+11%2A272730347.3+
+3%2A10%5E9+=+3000033820+
------------------------
The % error is:
+33820+%2F+%283%2A10%5E9%29+
This is a little more than
+10%5E4+%2F+10%5E9+=+10%5E%28-5%29+
+10%5E%28-5%29%2A100+=+10%5E-3+
Slightly more than .001 % off
I think it's close enough