Answers to growth homework.

1. Use the formula g=log(Nt/N0)/0.3 and you get g=17.7. So there must be
17.7 (or 18 rounded) generations to go from 500 to 108 CFU. Since the doubling
time is 20 min (0.33 hour), you get 18g x 0.33h/g = 5.9 h (or 6 h, rounded), so
you would have to come in at 5:00 pm + 6 h = 11:00 pm.

2. A. Same formula: g=log(48,000/3,000)/0.3 = 4.0;
5 h/4.0 g = 1.25 h/g or 75 min/g.

B. Growth rate is the inverse of the generation (doubling) time and is usually
denoted by the greek letter Mu (:). So the growth rate = 0.8/h or 0.013/min.

3. Now we are going to use Nt=N0 x 2g. First, we have to calculate the number
of generations (g) for each strain. The wild-type clone’s growth rate is 1.5g/h, so
in 10 h there are 15 generations. For the mutant clone the normal growth rate is
3g/h, so in 10 h there are 30 generations.

For the wild-type clone, N0=1000, so at 10 h, N10=1000 x 215 = 3.3x107 CFU.

For the mutant, N0=1, so at 10 h, N10=1 x 230 = 1.1x109 CFU.
So the ratio of wild-type to mutant clones is 3.3x107/1.1x109=0.03,
or about 1 in 33. Not very good!

4. Use g=log(Nt/N0)/0.3. g=log(1028/10-12)/0.3 = log1040/0.3 = 40/0.3 = 133.
Since each generation is 0.5 hours, it would take 133g x 0.5 hours = 67 hours or
roughly 2.8 days.