Question

Microbial Growth Write out the microbial growth equation and then use it to perform the calculations for the following scenario: If there are 200 bacterial cells in some salad at 1:00 PM and they double every 20 minutes, how many bacteria will there be at 6:00 PM. 22 = 4 23 = 8 24 = 16 26 = 64 27 = 128 28 = 256 29 = 512 210 = 1024 211 = 2048 212 = 4096 213 = 8192 214 = 16384 215 = 32768

Answer 1

Here the growth is by geometric progression. ie 1,2,4,8 ... or 20,21,22,...2n where n is the number of generations.

G=t/n is the equation from which calculations of generation time derives

G - Generation time

t - Time per generation in hours or minutes

n - Number of generations (number of times the cell population doubles during the time interval)

b =B x 2n (This equation is an expression of growth by binary fission)

b - number of bacteria at the end of the time interval

B - number of bacteria at the beginning of a time interval

n - number of generations (number of times the cell population doubles during the time interval)

Coming to the solution to the scenario

The mean division time for bacteria population is 20 minute.

The bacteria divide every 20 minutes, and will therefore divide three times every hour, 60/20 = 3.

If the bacteria grow for FIVE hours, each bacterium will divide 3 times per hour × 5 hours = 15 times.

To calculate the number of bacteria at the end of the growth period,use this equation b =B x 2n .

Number of bacteria at the beginning = 200

Number of divisions = 15

200 x 215  = 6553600  bacteria

in standard form it is written as 6.55 x 106 bacteria