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The number of bacteria present in a culture at time t hours is modelled by the

continuous variable N and the relationship

N = 2000e^(kt)

where k is a constant.

Given that when t = 3, N = 18 000, find

(a) the value of k to 3 significant figures

(b) how long it takes for the number of bacteria present to double, giving your

answer to the nearest minute

k is found to be 0.73241 to 5s.f

For the next part, i simply let N=18000*2=36000, and solved to find t=3.94 therefore it takes 3.94-3 = 0.94 hours for the number to double. This obviously yields the correct answer, however the markscheme let N=4000 subsequently solved to give 0.94 immediately (without having to subtract 3). Can someone please explain the logic behind the markschemes method?

Thanks