Question

The growth rate at t = 0 hours is bacteria per hour. When a bactericide is added to a nutrient broth in which bacteria are growing, the bacterium population continues to grow for a while, but then stops growing and begins to decline. The size of the population at time t (hours) is b = 65 +63t - 6242. Find the growth rates at t = 0 hours, t = 3 hours, and t = 6 hours. The growth rate at t = 3 hours is bacteria per hour. The growth rate at t = 6 hours is bacteria per hour. 22

Answer 1

given 3 2 2 b= 65 66 - 6 t b(t) = 65 +686 - 6² 2² Differentiate bll) with respect to t b' (t) = 6 - 2x6²t The growth rate at tzo hours b' (t) = 63 2X6²€ t-o bo) 2. 63 5 216 bacteria per hour the growth rate at ta3 hours bilt): 8 - 2 x 6² t 63 b (3) = 6² - 2x 6% 43 262 - 63 o bactena per hour 2

The growth rate at ta 6 hours 3 6' (t)? 6 - 2x 62 (26 666) = ² 2 x 6² x 6 = 6 - 2x6 :6 w 13 bacteña per hour 2 - 216 bactena