If a single bacteria divides in half every 20 min. how many would you have after 42 hours?
42 hours x (60 min/hr) = ?? minutes.
(??minutes/20 min)-1 = number of half lives.
2half-lives = number of bacteria. A large number. Check my thinking.
20min = 1/3 hour
42 hours therefore = 14 doublings
2^14 = 16,384
If the doubling is every 20 minutes, the way I see it is that gives 3 doublings every hour or 126 doublings in 42 hours. I think my earlier post should have omitted the -1 and 2(minutes/20)= number of bacteria.
I think Professor Damon made a math error:
42 hours= 126 doublings
2^126= 8.5*10^37
If you are using the exponential model...
Number=originalnumber*e^(.692time/timedoubled
Number= 1*e^(..693*42/(1/3))
number= e^(.693*126)=8.4E37 The difference with the 2^126 number is due to the approximation that ln 2=.693
Whoops, sorry, 42*3 not 42/3
Right. 2(42*60/20) = 2126 = 8.5E37
To determine the number of bacteria after 42 hours, we can break down the problem into steps:
Step 1: Convert 42 hours to minutes
There are 60 minutes in an hour, so to convert hours to minutes, multiply by 60:
42 hours * 60 minutes/hour = 2520 minutes
Step 2: Determine the number of divisions
Since the bacteria divided in half every 20 minutes, we need to find out how many times they divide within the time period.
Number of divisions = 2520 minutes / 20 minutes per division = 126 divisions
Step 3: Calculate the total number of bacteria
Starting with a single bacterium, each division doubles the number of bacteria. So, 1 division will result in 2 bacteria, 2 divisions will result in 4 bacteria, and so on.
Number of bacteria after 126 divisions = 2^126
To calculate this, you can use a calculator or use exponential notation to simplify the calculation:
2^126 = 850,705,917,302,346,158,658,436,518,579,420,528,128
Therefore, after 42 hours, you would have approximately 8.51 x 10^29 bacteria.