SOLUTION: Given a starting population of 100 bacteria, the formula b=100(2^t) can be used to find the number of bacteria, "b", after "t" periods of time. If each period is 15 minutes long, h

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Given a starting population of 100 bacteria, the formula b=100(2^t) can be used to find the number of bacteria, "b", after "t" periods of time. If each period is 15 minutes long, h      Log On


   

Question 578197: Given a starting population of 100 bacteria, the formula b=100(2^t) can be used to find the number of bacteria, "b", after "t" periods of time. If each period is 15 minutes long, how many minutes will it take for the population of bacteria to reach 51,200?
i already know the answer is 135...but how do you get that?
Found 2 solutions by dfrazzetto, josmiceli:
Answer by dfrazzetto(283) About Me  (Show Source):
You can put this solution on YOUR website!

b=100(2^t)
51,200 = 100 (2^t)
512 = 2^t
**take the log(base 2) of both sides
log(512) = log (2^t)
9 = t
so 9 'periods' of time, to get minutes:
minutes = 15t = 15 x 9 = 135 minutes

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+b+=+100%2A2%5Et+
given:
+b+=+51200+
+51200+=+100%2A2%5Et+
+512+=+2%5Et+
I noted that +2%2A2%2A2%2A2%2A2%2A2%2A2%2A2%2A2+=+512+
+512+=+2%5E9+, so
+2%5E9+=+2%5Et+
+t+=+9+
Every period of length +t+ is 15 min, so
+9%2A15+=+135+
It takes 135 minutes