A culture of bacteria contains 720 cells after 4 hours and 864 cells after 6 hours. Assume the number of cells in the culture grows exponentially.

a) How many cells were in the culture at the start?

b) What is the doubling time for the bacteria population? Give an answer in hours, rounded to one decimal place.

Question

A culture of bacteria contains 720 cells after 4 hours and 864 cells after 6 hours.  Assume the number of cells in the culture grows exponentially.

a) How many cells were in the culture at the start?

b) What is the doubling time for the bacteria population?  Give an answer in hours, rounded to one decimal place.

anonymous · Answer

I don't know how to start this problem...

anonymous · Answer

I'm thinking since it is exponential growth that I want to use the formula A = Pe^kt

anonymous · Answer

@kropot72

anonymous · Answer

There is 720 cells after 4 hours and there is 864 cells after 6 hours... so I'm not sure how to handle both of them

miracrown · Answer

So we assume an exponential growth for the bacteria. Because bacteria under go cell division in which one cell divides into two, we use "2" as the base of the exponential 

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So the way we can express this is as on the board.
N(t) = N_o 2^(t/t0) where N_o is the initial population size, and t0 is the doubling time.