Question

6. A bacteria culture grows at a rate proportional to its size. The initial population of the bacteria culture is 300 cells, and after 3 hours the population increases to 2400. (a) Find an expression for the number of bacteria after t hours. (b) When will the population reach 20000?

Answer 1

is The equation kt Plt) - Polt) e where Plt) any Population at time t population at time t = o Polt) - Given Polt) 300 At t = 3 Plt) 2460 from equation > k3 2400 350 3k :) 2400 300 In 8 In 123 ) In ( 134 ) > - > 3k = 3 ln2 -> k = ln 2 Pit) 300 elin2).t is the expression number for of bacteria t after hours .

tb) 2.0000 Plt) - from equation , (172).t 20000 300 e (in2),t 20006 200 3 300 both sides / Taking 'in' -) (In2), t in l 1200) ta 4.19970508 0.643147181 7 t 6.05889369 Answer i t 26.06 hours
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