A bacterial infection in an internal wound grows as `N'(t) = N_(0) 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 `(dN)/(dt)= -5 N^(2)`. What will be the plot of `N_(0)/N` vs. t after 1 hour?

Options

A.
B.
C.
D.

Answer

B

Explanation

Upto one hour
`N=N_(o) e^(t)` At t = 1 hour
`N=N_(o) e` After one hour `(dN)/(dt)=-5N^(2)`
`overset(N)underset(N_(o) e) int(dN)/(N^(2))=-5 overset(t) underset(1)intdt`
`[(1)/(N)]_(N_(o)e)^(N)=5[t]_(1)^(t) rArr (1)/(N) -(1)/(N_(o)e) =5 (t-1) rArr (1)/(N) =5t -5 +(1)/(N_(o) e)`
Multiply `N_(o)` both side
`(N_(o))/(N) =5N_(o) t+((1)/(e)-5N_(o)) rArr y=m x+ c`