JEE Main 2022 · 30 Jun · Shift 1 · Mathematics Q26

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MathematicsInteger+4 / -1Question 26 of 90

A hostel has 100 students. On a certain day (consider it day zero) it was found that two students are infected with some virus. Assume that the rate at which the virus spreads is directly proportional to the product of the number of infected students and the number of non-infected students. If the number of infected students on 4 $^{\text{th}}$ day is 30, then number of infected students on 8 $^{\text{th}}$ day will be ______.

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Answer and worked solution

Official answer: 90

Logistic growth. $\dfrac y{100-y}=\dfrac2{98}e^{100kt}$ . Day 4: $\frac{30}{70}=\frac1{49}\times21$ , so the factor per 4 days is 21.

Day 8. $\frac1{49}\times441=9$ , so $y=90$ .

Answer: 90

Topics:Formation and applications Variable separable

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JEE Main 2022 · 30 Jun · Shift 1, Mathematics question 26