Question

The population (in thousands) of a colony of bacteria t minutes after the introduction of a toxin is given by the function.P(t) =
t^2 + 4 if 0 ≤ t < 5
−5t + 54 if t ≥ 5.
When does the colony die out?

Answer 1

The colony die out when the population becomes 0. i.e. P(t) = 0.
-5t + 54 = 0
5t = 54
t = 54/5
t = 10.8

Therefore, the collony will die out after 10.8 minnute (10 minutes 48 seconds)

Answer 2

P(t)=$-5t+54$
When t= 11 or exceeds 11, then the colony dies out.
ie 
p(11)=-5(11)+54
P(11)=-55+54
P(11)=-1