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.