Question

A researcher withdraws 12 mL of culture 7 hours after inoculation, which has a cell concentration of 1.5 x 109 cells/mL. After centrifugation and discarding the supernatant, how much tryptone broth, in mL, should she use to resuspend the pellet to obtain a concentration of 3.5 x 109 cells/mL?

The answer is 5.1 mL but need to show work.

Answer 1

the concentration of the initial culture= 1.5x 10^9 cells/mL

number of cells in 12 mL= volume of the culture concentration

= 121.5x 10^9

= 1.810^10 cells.

final concentration= 3.5 x 10^9 cells/mL

final concentration= number of cells taken/volume of the final solution

number of cells take = 1.810^10 cells.

3.5 x 10^9 cells/mL =1.810^10/ volume of the final solution

volume of the final solution = 1.810^10/3.5 x 10^9

= 5.1 mL

so the answer is 5.1 mL