Question

Growth 1) An infectious bacterium enters the bloodstream of an unsuspecting wild lynx. A ranger a serum that kills the bacteria. The serum immediately kills 10% of the bacteria, and the remaining population has a half life of 9 hours. For the lynx to be stable to return to the wild, only 25% of the bacteria can remain. Find how long it will take after injecting the serum for the lynx to be stable enough to return to the wild. finds the ill lynx and injects Decay

Answer 1

The growth or decay of the bacteria population after injecting a serum is governed by the equation N = Ne-at Where No = number of bacteria in the bloodstream of an unsuspecting wild lynx at time t = 0, As the serum immediately kills 10% of the bacteria, N, = 0.9 N = number of bacteria left after time t. Also the remaining population has a half life of 9 hours. So after 9 hours N = 0.5 Thus substituting these values we get 0.5 = 0.9e-92 0.5 e-91 = 0.555 0.9