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 5.75 x 106 cells/mL. How many cells should be present after 8 generations in a 1 mL culture, if the initial cell culture had an absorbance reading of 1.25

18.38 × 10⁸.

Explanation:

Absorbance of the cell is directly proportional to their number

A\alpha cells/mL

A=K ×cells/mL ( Here, K is a constant)

so A/ (cells/mL)=K

so A1/( cells/mL)1=A2/ ( cells/mL)2

Here, A1 is initial absorbance, (cells/mL)1= initial concentration, (cells/mL)2= final concentration, A2= final absorption

so ( cells/mL)2=(A2* (cells/mL)1 ) / A1

= (1.25 × 5.75 ×10⁶)/1

= 7.18 ×10⁶.

so final concentration of bacteria in the culture having an absorbance of 1.25 =  7.18 ×10⁶.

so the number of cells after 8 generations

The cell growth is geometrically ,  after one generation the number of cell doubles, and after a second-generation number of cells becomes 4 times that of initial concentration.

the nth term of geometric progression=arⁿ⁻¹

Here, a is the first term, r =2 ( r=nth term/ (n-1) th term)

here n=9 ( n= number of generations+1)

so 9th term= (7.18 ×10⁶ × 2⁸)

= 18.38 × 10⁸.

so number of cells in 1 mL after 8 generations= 18.38 × 10⁸.

Thus, the answer is 18.38 × 10⁸.