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mario62 [17]
3 years ago
14

A culture of bacteria enters the exponential growth phase with 4,596 cells per mL. After 15 hours, there are 206,104,972 cells p

er mL. What is the instantaneous growth rate constant, with units of 1/hours, for this culture? Express your answer as an exponent rounded to two decimal places. For example 0.66666 would be entered as 6.67E-1
Biology
1 answer:
tekilochka [14]3 years ago
6 0

Answer:

The Growth rate constant (k) will be = 5.16 \times 10^-03  per minute or 0.308  per hour.

Explanation:

Given,

N₀ = 4596 cells / ml

N = 206104972 cells / ml

t = 15 hours

We know that,

                  n = 3.3 \times log  \frac {b}{B}

Where,

n = no. of generation during the period of exponential growth.

∴    n = 3.3 \times log  \frac {b}{B}

       = 3.3 \times log \frac {206104972} {4596}

       = 3.3 × 44844.42

∴   n  = 15.350

We know that,

                 g = \frac {t} {n}

Where,

g =  generation time    

t = duration of exponential growth

∴    g = \frac {t} {n}                             or                ∴    g = \frac {t} {n}

         =  \frac {15 \times 60} {15.350}                                               = 15 / 15.350

          = 900 / 15.350                           ∴  g  = 0.977 hours

∴      g  = 58.63 minutes

We know that,    

               k = 0.301 / g

Where,   k = specific growth rate

∴    k = 0.301 / g                       or                      ∴   k = 0.301 / g  

           = 0.301 / 58.63                                            = 0.301 / 0.977

∴      k   = 5.16 \times 10^-03  per minutes             ∴  k   = 0.308 per hour

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