Question

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(3 points) A bacteria culture initially contains 200 cells and grows at a rate proportional to its size. After an hour the population has increased to 500 Find an expression for the number Pt) of bacteria after t hours. P(t) = 200e"(In(5/2jt) Find the number of bacteria after 2 hours. Answer: 1250 Find the rate of growth after 2 hours. Answer: In(5/2) When will the population reach 20000? Answer (In(100)/(In(5/2))

Answer 1

let Peel be the populatiou . dP - KP. dt Given plo)= 200 PCIe 500. aby = fkdt en pl = kt te Pa pkt a ee P - E pkt. Given Plo) = 200 200 = a IP = 2000 kt : 500 - 200 e kli) - etas 7 keen (A) = Tp. 200 elenca)+] | PCOS 200 260-9163t)) Pre) - 200 (0.9163)2) = 1250.023 - 1250) 1250

Rate of growth is dp = kP. dt growth rate after 2 hrs. de & = kxp (2) 1250 x en (5) 11 45. 4 2000din - 200 e com Co. 9163t) 0.9163t. 100 2 0.9163t- en Croo) ta en croo) - 15.026 h 26 thos 0.9163 en (100) en (S).