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)= (piecewise) t^2+1 if 0(greater than or equal to)t<5
-8t+66 if t is greater than or equal to 5

a. When does the colony die out?
b. Show that at some time between t=2 and t=7, the population is 9,000

Answer 1

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.