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30 January, 08:24

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

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  1. 30 January, 09:18
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    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.
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