SOLUTION: A colony of bacteria originally contains 800 bacteria. It doubles in size every 30 minutes. How many hours will it take for the colony to contain 8,000 bacteria? (Round your answer

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: A colony of bacteria originally contains 800 bacteria. It doubles in size every 30 minutes. How many hours will it take for the colony to contain 8,000 bacteria? (Round your answer      Log On


   

Question 1057608: A colony of bacteria originally contains 800 bacteria. It doubles in size every 30 minutes. How many hours will it take for the colony to contain 8,000 bacteria? (Round your answer to one decimal place.)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +P+ = the population of bacteria at
time +t+ in hrs with a starting population
of +800+ bacteria
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+P+=+800%2A2%5E%282t%29+
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What is +t+ when +P+=+8000+
+8000+=+800%2A2%5E%282t%29+
+10+=+2%5E%282t%29+
Take the log base 10 of both sides
+1+=+%282t%29%2Alog%282%29+
+1+=+.301%2A%282t%29+
+t+=+1%2F.602+
+t+=+1.66+ hrs
+t+=+1.7+ hrs
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check:
+8000+=+800%2A2%5E%282t%29+
+8000+=+800%2A2%5E%282%2A1.66%29+
+10+=+2%5E3.32+
+10+=+9.987+
error due to rounding off, I think
OK