The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. After 3 hours it is observed that 400 bacteria are present.

Question.

The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time . After 3 hours it is observed that 400 bacteria are present. After 10 hours 2000 bacteria are present. What was the initial number of bacteria?

 

Solution:

 

 

 

Population is 400 after 3 hours i.e.

i.e.                      …………………(1)

 

Population is 2000 after 10 hours i.e.

i.e.                                          …………..(2)

 

From eq. (1) we get

From eq. (2) we get

 

Compare above two equations and solve for

 

Put in eq. (1) to get initial population of Bacteria