# To calculate: The number of days after which, 250 students are infected by flu virus in the college campus containing 5000 students. If one student re

To calculate: The number of days after which, 250 students are infected by flu virus in the college campus containing 5000 students. If one student returns from vacation with contagious and long- lasting flu virus and spread of flu virus is modeled by $y=\frac{5000}{1+4999{e}^{-0.8t}},t\ge 0$.
Where, yis the total number of students infected after days.
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Calculation:
Algebraic solution
Consider the model equation to represent the spread of flu virus,
$y=\frac{5000}{1+4999{e}^{-0.8t}},t\ge 0$
Where, y is the total number of students infected after days.
Now, calculate the number of days after which 250 students are infected.
Put $y=250$ in the model equation.
$250=\frac{5000}{1+4999{e}^{-0.8t}}$
Divide by 250 and multiply by $1+4999{e}^{-0.8t}$ each side.
$1+4999{e}^{-0.8t}=\frac{5000}{250}$
$1+4999{e}^{-0.8t}=20$
Subtract 1 from each side.
$4999{e}^{-0.8t}=19$
Divide by 4999 as,
${e}^{-0.8t}=\frac{19}{4999}$
Take natural logarithm each side as,
${\mathrm{ln}e}^{-0.8t}=\mathrm{ln}\left(\frac{19}{4999}\right)$
By inverse property,
$-0.8t\sim eq-5.5726$
Divide each side by -0.8 as,
$t\sim eq\frac{5.5726}{0.8}$
$\sim eq6.96575\sim eq7$
Thus, after about 7 days, 250 students are infected.
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