SOLUTION: I have asked a question similar to this in the past, but its works still elude me... A population of a colony of bacteria grows expodentially with time. At start of experiment t

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Question 556207: I have asked a question similar to this in the past, but its works still elude me...
A population of a colony of bacteria grows expodentially with time. At start of experiment there are 6000. 1 hr later there are 6500. How long before it reaches 9500. Need exact and numerical approximation...
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A population of a colony of bacteria grows exponentially with time.
At start of experiment there are 6000. 1 hr later there are 6500.
How long before it reaches 9500. Need exact and numerical approximation...
:
Find k
6000*(1+k) = 6500
1 + k = 6500%2F6000
1 + k = 1.0833
k = 1.0833 - 1
k = .0833
:
Find t
6000*(1+.0833)^t = 9500
1.0833^t = 9500%2F6000
1,0833^t = 1.5833
t*ln(1.0833) = ln(1.5833)
t = ln%281.5833%29%2Fln%281.0833%29
t = 5.74 hrs to reach 9500 (from 6000)