The bacteria culture grows at a rate proportional to its size After 2 hours, there are 600 bacteria and after 8 hours the count is 75000. FInd the initial population and when will the population reach 200000?

Question

The bacteria culture grows at a rate proportional to its size After 2 hours, there are 600 bacteria and after 8 hours the  count is 75000. FInd the initial population and  when will the population reach 200000?

isaidavila · Answer

When says the rate of grow is proportional  to the size
dP/dt=kP
Solving this differential equation we got:
P=Po*e^(kt)
Where Po  is the initial population 
And t is the time passed.
Replacing P=600 and t=2, P=75000 and t=8 to find k.