Estimates the number of E. coli, N, of an initial sample of No bacteria after t minutes, at 37 degrees

Question

N= No X t/220 

estimate the number of E. Coli, N, of an initial sample of No bacteria after t minutes, at 37 degrees (body temperature) under optimal conditions.

How long does it take for E. coli to double in size? 

 

Answer 1

Assuming that this is a standard exponential growth equation

 

N = N₀ e^rt

 

Since the growth is doubled, N/N₀ = 2

 

2 = e^rt

 

or 

 

2 = e^t/220

 

Take the natural log of both sides

 

ln 2 = t/220

 

0.693 = t/220

 

152.49 = t 

 

So it takes 152.49 minutes to double in size