Q.

A bacterial infection in an initial wound grows N01(t)=exp(t), where the time t is in hours A dose of antibiotic, taken orally, needs 1 hour to reach the wound. Once it reaches there, the bacterial population goes down as dNdt=-5 N2 What will be the plot of N0 NVs t after 1 hour

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a

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b

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c

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d

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answer is A.

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Detailed Solution

 From o to 1 hour, N=N0et  From 1 hour onwards dNdt=5N2  So at t=1 hours, N=eN0 dNdt=5N2  eN0NN2dN=51tdt 1N1eN0=5(t1) N0N1e=5N0(t1) N0N=5N0(t1)+1e N0N=5N0t+(1e5N0) which is following y=mx+C 

Therefore, the correct option is (A).

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