SOLUTION: Two crafty bacteria fall into a pot of milk which has recently been sterilized. They reproduce at a rate of 4% per day. Determine how many bacteria will be present after 100 days.

Question 124288: Two crafty bacteria fall into a pot of milk which has recently been sterilized. They reproduce at a rate of 4% per day. Determine how many bacteria will be present after 100 days.
A 100
B 800
C 0
D 2
E 109
F 345
I'm really stuck on this problem because I'm not sure where to start. I would really apprciate it if someone could walk me through the steps to get to the correct answer,thank you in advance for your time.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Two crafty bacteria fall into a pot of milk which has recently been sterilized. They reproduce at a rate of 4% per day. Determine how many bacteria will be present after 100 days.
A 100
B 800
C 0
D 2
E 109
F 345
---------------------------
Day 1: 2
Day 2: 2+0.04*2=2(1+0.04)= 2*1.04
Day 3 = (2*1.04)+0.4*(2*1.04) = 2*1.04(1+0.04) = 2*(1.04)^2
....
...
Day 100 = 2*1.04^99 = 97
---------------
Cheers,
Stan H.

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