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The population (in thousands) of a colony of bacteria t minutes after the introduction of a toxin is given by the function


P(t)= (piecewise) t^2+1 if 0(greater than or equal to)t<5

-8t+66 if t is greater than or equal to 5

AWhen does the colony die out?
BShow that at some time between t=2 and t=7, the population is 9,000

Verified Answer :

nobillionaireNobley

The colony will die out when P(t) = 0.
-8t + 66 = 0
8t = 66
t = 66/8 = 8.25
The colony will die out after 8.25 seconds.

P(t) = t^2 + 1 = 9
t^2 = 9 - 1 = 8
t = sqrt(8) = 2.83 minutes.

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