Respuesta :
Answer:
The Growth rate constant (k) will be = [tex]5.16 \times 10^-03[/tex] Â per minute or 0.308 Â per hour.
Explanation:
Given,
Nâ‚€ = 4596 cells / ml
N = 206104972 cells / ml
t = 15 hours
We know that,
         n = [tex]3.3 \times log \frac {b}{B}[/tex]
Where,
n = no. of generation during the period of exponential growth.
∴   n = [tex]3.3 \times log \frac {b}{B}[/tex]
    = [tex]3.3 \times log \frac {206104972} {4596}[/tex]
    = 3.3 × 44844.42
∴  n  = 15.350
We know that,
         g = [tex]\frac {t} {n}[/tex]
Where,
g =  generation time  Â
t = duration of exponential growth
∴   g = [tex]\frac {t} {n}[/tex]               or         ∴   g = [tex]\frac {t} {n}[/tex]
     =  [tex]\frac {15 \times 60} {15.350}[/tex]                        = 15 / 15.350
     = 900 / 15.350              ∴  g  = 0.977 hours
∴    g  = 58.63 minutes
We know that, Â Â
        k = [tex]0.301 / g[/tex]
Where, Â k = specific growth rate
∴   k = [tex]0.301 / g[/tex]            or            ∴  k = [tex]0.301 / g[/tex] Â
      = 0.301 / 58.63                       = 0.301 / 0.977
∴    k  = [tex]5.16 \times 10^-03[/tex]  per minutes       ∴  k  = 0.308 per hour
