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

Question

Luna Gill

Mathematics

14 April, 19:48

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

+3

Answers (1)

Know the Answer?

Santos Newton · 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.