SOLUTION: the number of bacteria in a certain culture is given by the function b(t)=10000e^.04t where t represents time in hours. how long will it take for the number of bacteria to reach

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Question 1040022: the number of bacteria in a certain culture is given by the function b(t)=10000e^.04t
where t represents time in hours. how long will it take for the number of bacteria to reach 15000. round to nearest hundredth
Found 2 solutions by ankor@dixie-net.com, solver91311:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
the number of bacteria in a certain culture is given by the function b(t)=10000e^.04t
where t represents time in hours. how long will it take for the number of bacteria to reach 15000. round to nearest hundredth
:
10000%2Ae%5E%28.04t%29+=+15000
divide both sides by 10000
e%5E%28.04t%29+=+15000%2F10000
e%5E%28.04t%29+=+1.5
using natural logs
ln%28e%5E%28.04t%29%29+=+ln%281.5%29
log equiv of exponents
.04t*ln(e) = ln(1.5)
the nat log of e is 1. find the nat log of 1.5
.04t = .405465
t = .405465%2F.04
t = 10.34 hrs to reach 15,000

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!












is the exact answer. Use your calculator to find an approximation to whatever precision you desire.

John

My calculator said it, I believe it, that settles it