An amoeba propagates by simple division; each split takes 3 minutes to complete. When such an amoeba is put into a glass container with a nutrient fluid, the container is full of amoebas in one hour. How long would it take for the container to be filled if we start with not one amoeba, but two?

Question

An amoeba propagates by simple division; each split takes  3 minutes to complete. When such an amoeba is put into a glass container with a nutrient fluid, the container is full of amoebas in one hour. How long would it take for the container to be filled if we start with not one amoeba, but two?

allank · Answer

I think the population of amoeba in the container can be modeled by the exponential equation: p(t)=p_o*e^(kt) where p_o=initial population. From the question, p_o=1, and p(3)=2. So have p(3)=1*e^(3k)=2 thus 3k=ln(2) and k=ln(2)/3. 
Now we have an equation that gives us the population at any time:
p(t)=p_o*e^(kt) where p_o=initial population, k=ln(2)/3, and t is in minutes.
Can you take it from there?