It takes 12 hours for a certain bacterial culture to double in population

Question

P=P₀e^rt

Answer 1

I assume the question is to find r.

 

Let T = the time it takes to double, given as 12 hours.

 

exp[r(t + T)] = 2 exp(rt)

 

exp(rt) * exp(rT) = 2 exp(rt)

 

exp(rT) = 2

 

rT = ln(2)

 

r = ln(2) / T = ln(2) / (12 hours)