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You make a dilution by transerring 1 mL of a culture into 99 mL of saline. You then repeat the operation by transferring 1 mL of the diluted culture into another 99 mL bottle of saline. When you inoculate an agar late with 1.0 mL of the final dilutionand obtain 85 colonies. What was the concentration cells in the orginal culture?

A. 8.5x10^2
B. 8.5x10^3
C. 8.5x10^4
D. 8.5 x10^5
E. 8.5x10^6

A culture was inoculated with 1 x 104 bacteria. After 1 hour and forty miutes the culture was sampled and found to have 1 x 107 cells. What is the generation time of  the bacteria in the culture?

For the first question, recall the equation CiVi=CfVf. where i = initial and f = final
 
3 dilutions were performed, so to elaborate the above equation: C1V1=C2V2=C3V3.

In each dilution, the initial volume is 1mL and the final volume is 100mL (1mL+99mL of saline solution).
-We know our 3rd final volume and bacterial concentration: 85 colonies per 1mL (85col./1mL) and we must work backwards: C2iV2i=C3fV3f
Therefore, C3f=85 and V3f=100mL and V2i
-Solve for C2i from C2i=(C3fV3f)/V2i---> C2i=(85col.x100mL)/1mL---> C2i=8500col.

Now, C2iv2i becomes C2fV2f, since we are solving for the first dilution. So C2f is 8500col. and V2f will be 100mL, since it is a final volume from the first dilution, and V1i is 1mL, because we are adding it to the first 99mL of saline solution.

C1iV1i=C2fV2f ---> C1i = (C2fV2f)/C1i ---> C1i = (8500col.x100mL0/1mL ---> C1i = 850000 or 8.5x10^5

Post Merge: 11 years ago

For the second question:
Equation for generation time (G) is:
G=t/n, where (t) is time in minutes and (n) is number of generations.
Recall also that the equation for bacterial growth by binary fission is:
b = (2^n)B, where (b) is # bacteria at end of time interval and (B) is # bacteria at beginning of time interval.

-Because we are given b and B, solve for n and plug it into generation time equation.

b/B=(2^n)
logb = logB + nlog2
n = logb - logB
           log2

so n = [(log1e7)-(log1e4)]/log2 ---> n=0.807354

for generation time: n=0.807354 and t=100min
G=100min/0.807354
G=123.861262 ---> G=100min if you account for corret sig figs