The number of days so that half the population have flu is

50

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40

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45

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25

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Solution

The correct option is B $40$
Let N be the no. of people having the disease
$\frac{d N}{d t} = k N (25000 - N)$
Integrating
$- l n (25000 - N) + l n (N) = 25000 k t + c$
$l n \frac{N}{25000 - N} = 25000 k t + c$
Using the condition given
$t = 0, N = 100$
$c = l n \frac{1}{249}$
$l n \frac{249 N}{25000 - N} = 25000 k t$
$t = 10, N = 400$
$l n \frac{249 \times 4}{246} = 250000 k$
25000k =0.138
Now time taken for half the population to have the flu
N =12500
$l n 249 = 25000 k t$
$t = 40 d a y s$

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