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99 Percentile Qs Bank for JEE MainMathematicsApplication of Derivatives

Let y be the number of people in a village at time t. Assume that the rate of change of the population is proportional to the number of people in the village at any time and further assume that the population never increase in time. Then, the population of the village at any fixed t is given by

Options

  1. Ay = e k t + c , for some constants c ≤ 0 and k ≥ 0
  2. By = c e k t , for some constants c ≥ 0 and k ≤ 0
  3. Cy = e c t + k , for some constants c ≤ 0 and k ≥ 0
  4. Dy = k e c t , for some constants c ≥ 0 and k ≤ 0

Correct answer

B. y = c e k t , for some constants c ≥ 0 and k ≤ 0

Step-by-step solution

Given, d y d t ∝ y , w h e r e y is the position of village ⇒ 1 y d y = k d t ⇒ log ⁡ y = log ⁡ c + k t [on integrating] ⇒ log ⁡ y c = k t ⇒ y = c e k t

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