A bacterial infection in an internal wound grows as N'(t) = N₀exp(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 = −5N². What will be the plot of N₀/N vs. t after 1 hour?<p></p>

The correct option is A
Solution:- (A)
From 0 to 1 hour, N' = N₀eᵗ
From 1 hour onwards
dN/dt = −5N²
So at t = 1 hour, N' = eN₀
dN/dt = −5N²
∫N⁻²dN = −5∫₁ᵗ dt
N⁻¹/(-1)|eN₀ = 5(t-1)
-1/N|eN₀ = 5(t-1)
-1/eN₀ + 1/N = 5(t-1)
1/N = 5(t-1) + 1/eN₀
N₀/N = 5N₀(t-1) + 1/e
N₀/N = 5N₀t + (1/e - 5N₀)
which is following y = mx + C

Eduprobe

Question:

A bacterial infection in an internal wound grows as N'(t) = N₀exp(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 = −5N². What will be the plot of N₀/N vs. t after 1 hour?

Solution: