SOLUTION: A single microscopic organism divides into two organisms every 3 days. Use the formula N(t)= No(2)^t/3 Where t is the time of day , N(t) is the number of organisms at t days

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Question 391214: A single microscopic organism divides
into two organisms every 3 days. Use
the formula N(t)= No(2)^t/3
Where t is the time of day ,
N(t) is the number
of organisms at t days, and No is
the number of organisms at t = 0.
Approximately how long would it
take one organism to produce a
population of about 10,000 organisms?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
N%28t%29+=+N%5B0%5D%2A2%5E%28t%2F3%29
given:
N%5B0%5D+=+1
N%28t%29+=+10000
----------------
10000+=+1%2A2%5E%28t%2F3%29
Take the log of both sides
log%2810000%29+=+%28t%2F3%29%2Alog%282%29
4+=+.30103%2A%28t%2F3%29
t%2F3+=+13.2877
t+=+39.863
About 39 days and 21 hours
check answer:
10000+=+1%2A2%5E%28t%2F3%29
10000+=+1%2A2%5E%2839.863%2F3%29
10000+=+2%5E13.2877
10000+=+9999.683
close enough