Question 1096997
The formula for exponential decay here is P(t)=P(0)e^-kt, where P(t) is the resultant population,P(0)is the initial population, k is the decay constant, and t is the time. So, in the case of half-life, P(t)/P(0)=.5, and t here is 14 days. So:
.5=e^-14k
ln 0.5=ln e^-14k=-14k ln e=-14k
k=0.04951051289713895067265943724701
For there to be 5 zulus left, we have:
5/20=e^-0.04951051289713895067265943724701t
.25=e^-0.04951051289713895067265943724701t
ln 0.25=ln e^-0.04951051289713895067265943724701t=-0.04951051289713895067265943724701t (ln e)=-0.04951051289713895067265943724701t
t=ln 0.25/-0.04951051289713895067265943724701=28 days
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