# Bacterial Growth

• March 7th 2009, 05:41 PM
clemkonan
Bacterial Growth
I need a refresher on how to calculate bacterial growth when the generation time is known. If a cell double every 4 hour then at 8 hours we have 2 cells at16 hours we have 4 at 32 hours 8 etc.

My task is to calculate what the population would be if I am starting with 20 cells , the generation or doubling time is 4 hours and 14 days has elapsed?

Thanks
• March 7th 2009, 05:51 PM
e^(i*pi)
Quote:

Originally Posted by clemkonan
I need a refresher on how to calculate bacterial growth when the generation time is known. If a cell double every 4 hour then at 8 hours we have 2 cells at16 hours we have 4 at 32 hours 8 etc.

My task is to calculate what the population would be if I am starting with 20 cells , the generation or doubling time is 4 hours and 14 days has elapsed?

Thanks

$N(t) = N(0)\cdot 2^{t/4}$

N(t) is the amount at time t
N(0) is the amount at the start (20)
2 is because it's doing up in powers of 2
t/4 because it doubles every 4 years now every year.

$N(t) = 20\cdot 2^{\frac{14*24}{4}} = 3.87x10^{26}$
• March 7th 2009, 06:10 PM
clemkonan
Bacterial Growth
Thanks, this is fantastic
• March 7th 2009, 06:25 PM
clemkonan
I think there is a typo at t/4 , 14 days gives us 84 generations not sure of the reference to "year"