Before the Propionbacteria being to multiply, their population includes 2500 ind

Question

Before the Propionbacteria being to multiply, their population includes 2500 individuals. Use a logistic curvre to model their growth (rmax=1.1) K=4x10^4 and time is in days.

(a) Calculate the size of the population 4 days after they begin to multiply.

Other related information: Propionbacteria being to multiply only whenthe Lactobacilllus population reaches 5x10^5 individials which is 4.3 days. Exponential equation for Lactorbacillus is Nt=4300e^(1.2) t

Please show your work.

Explanation / Answer

dP/dt = rP(1-P/K) K = 4*10^4 rmax = 1.1 P(t) = (KP0e^rt)/(K+P0(e^rt-1)) P0 = 2500 r = 1.1 t is time in days K = 4*10^4 Therefore P(t) = (4*10^4*2500*e^1.1t)/(4*10^4+2500(e^1.1t-1)) =>P(4) = (4*10^4*2500*e^(1.1*4))/(4*10^4+2500((e^(1.1*4))-1)) = 33779

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