Question

Bacteria usually reproduce by a process called binary fission. In this type of reproduction, one bacterium divides to form two bacteria. Under ideal conditions, some bacteria reproduce every 15 minutes. Find the constant k for this type of bacteria under ideal conditions. Assume t is in minutes.

Answer 1

`k = 0.462`

Step-by-step explanation:

Given-

A bacteria reproduces after every fifteen minutes.

Thus, after every fifteen minutes, the bacterial population will get double.

Now as we know that

`N_t = N_o e^(kt)`

Here,

`N_t` represents the population after time t

`N_o` represents the initial population

Substituting the given values in above equation we get -

`(N_t)/(N_o) =2\\`

`2 = e^{15k]`

`15k = ln 2`

On solving we get -

`k = (ln 2)/(15)`

`k = 0.462`

Answer 2

K= 0.067 per minute

Step-by-step explanation:

This was obtained from the equation k= (Log Nt - Log No) / (0.301 x t)

where Nt = 2, No = 1 and t = 15

therefore, k = ( Log 2 - Log 1) / (0,301 x 15)

then k = 0.301 / 0.301 x 15

k = 1 / 15

Finally, K = 0.067m^{-1}