Find a function that gives the number of bacteria present in the colony after t hours.

Question

Suppose that a colony of bacteria starts with 1 bacterium and doubles in number every half an hour.

(a) Find a function that gives the number of bacteria present in the colony after t hours.

(b) When will there be 256 bacteria in the colony?

Answer 1

a) This is an example of exponential growth: N=N₀2^t/(1/2) or 2^2t (N₀=1)

b) solve for t: t = ln(N/N₀)/ln(2) plugging in N = 256

or use the fact that 256 = 2⁸ , so 2t = 8