Respuesta :
Answer:
The Growth rate constant (k) will be = [tex]5.16 \times 10^-03[/tex] per minute or 0.308 per hour.
Explanation:
Given,
N₀ = 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
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,
k = [tex]0.301 / g[/tex]
Where, k = specific growth rate
∴ k = [tex]0.301 / g[/tex] or ∴ k = [tex]0.301 / g[/tex]
= 0.301 / 58.63 = 0.301 / 0.977
∴ k = [tex]5.16 \times 10^-03[/tex] per minutes ∴ k = 0.308 per hour
