Question

the baacteria culture grow at a rate proportional to its size . after 2 hours there are 600 bacteria and after 8 hours the count is 75000. Find initial population and when will the population reach 200000.?

Answer 1

Answer:

P(t) = P(0) k^t

(OR P(t) = P(0) . exp[ln(k) . t] . )

P(2) = P(0) k^2 = 600

P(8) = P(0) k^8 = 75000

P(8)/P(2) = k^6 = 75000/600 = 125, so k = sqrt(5)

i) P(0) = 600/k^2 = 600/5 = 120

P(t) = 120 . 5^(t/2)

P(t) = 120 . 5^(t/2) = 200000

5^(t/2) = 200000 / 120

(t/2) = ln(200000 / 120) / ln(5)

t = 2 . ln(200000 / 120) / ln(5) = 9.2 hrs