Question

Based on prior experiments, you have determined that for a culture of S. aureus an absorbance reading of 1.0 AU₆₅₀ is approximately equal to 4.5 x 10⁶ cells/mL.

How many cells should be present after 7 generations in a 1 mL culture, if the initial cell culture had an absorbance reading of 1.25? (3 Points)

Answer 1

number of cells in the initial culture

absorbance is directly proportional to the concentration of bacterial cells

so Absorbance is A and concentration is C K = constant

A= KC

A/C=K

for A=1 C=4.5*10^6 cells/mL

so A/C=1/(4.5*10^6)

initial culture has absorbance = 1.25

so concentration C we have to find

1.25/C=1/(4.5*10^6)

so C= 1.25*4.5*10^6

= 5.625 *10^6 cells/ mL

cells after 7 generations in 1 mL

after one generation number of bacteria doubles so as bacteria grows the number increases like geometric progression

of r=2 ( r=nth term/n-1 th term)

so nth term= ar^n-1 ( a is the first term, here a= 5.625 *10^6, r=2 and n=8, after 7 rounds, including the first term there will be 8 terms)

8th term= 5.625 *10^6 * 2^7

= 720*10^6

so number of bacteria that will be present after 7 rounds of replication is 7.20*10^8 cells.

so number of cells