How many bacteria will there be after 9 hours, 11 hours, and 14 hours?

Question

A science experiment shows that the numbers of bacteria in a Petri dish will double every hour. There are 1000 bacteria after 8 hours 

Answer 1

Nora,

 

The (exponential) growth equation is: N(t) = N(t=0) exp( kt ), where N(t) is the number of bacteria at time t in hours.

 

Knowing that the number of bacteria doubles every hour allows us to write: N(t=1)/N(t=0) = 2 = exp( k * 1 ) or ln( 2 ) = 0.693 = ln[exp( k )] = k.

 

Knowing that there are 1000 bacteria after 8 hours allows us to write: N(8) = 1000 = N(t=0) exp( 0.693 * 8 )   or  N(t=0)  = exp( 0.693 * 8) / 1000 ~ 2.

 

So, you can calculate N(t) = 2 * exp( 0.693 * t ) for t=9, t=11, and t =14.

 

Michael.