You measure 85000 bacteria initially If the growth rate mu

You measure 85,000 bacteria initially. If the growth rate mu = 1.5/hr, how long will it take for the number of bacteria to reach and 1,800,000? 4b. If the generation time for the bacteria is 2 hours, how long will it take for the number of bacteria to reach 1,800,000?

Solution

a) Nt = N0 x [1 +r]^t where Nt is the population after time t , N0 is the initial population and r is the rate of multiplication. Here r = u = 1.5/hr

1800000= 85000 x [1 +r]^t

[1 +r]^t = 1800/85 now taking log on both sides

log [1 +r]^t = log 1800/85

t x log [1 +r]= log1800 – log85

t x log [1+1.5] =3.25-1.92

t x log 2.5 = 1.33

t x 0.4 = 1.33

t = 1.33/0.4

t= 3.32 hrs.

b) If generation time G is 2 hours then,

G = t/[3.3 log B/A]   where t is total time and B is final population and A is initial population

2 = t/ [3.3 x log 1800/85]

2 = t/ [3.3 x 1.33]   [from above calculations]

t =2 x 4.4 = 8.8 hours.