i don’t understand how to do doubling

Question

The count in a bacteria culture was 300 after 10 minuets and 1900 after 30 minuet. assuming the count grows exponentiall,  what is the initial siz of the cultur?, find the doubling perio?, find the population after 90 minuet?, when will the population reach 15000

Answer 1

Kaobi,

 

Remember that earlier problem with the radioactive goo and half-life?  This problem is actually similar, only instead of half-life, we work with doubling period.

 

P(t) = P₀ (2)^t/T

 

T = doubling period in minutes, t = time elapsed in minutes from the time when when P(t) was P₀

 

Since we do not know what P was at t=0, let us reset the clock and make t=10 min the start time.

 

At 10 min, P₀ = 300

At 30 min, which is 20 min after 10 min, P = 1900.  The elapsed time is 20 min, not 30 min.

 

P(20) = 300 (2)^20/T = 1900

 

(20/T)log2 = log(1900/300)

 

T = 20 log2 / log(1900/300) ≅ 7.51 min

 

A(t) = 300 (2)^t/7.51

 

t = minutes after 10 min.

 

Can you finish from here?  Remember that 90 min is really 80 min if you use 300 for P₀.  Similarly, when you calculate how long it takes to reach 15000, remember that is time elapsed after the first 10 min.