Verified Solution • 2025–26 Session moderate

QJEEM21Ma635b: JEE Main 2021 Mathematics - Class 12 JEEM21Ma635b Solution: The population P = P(t) at time 't' of a certain species…

The population P = P(t) at time 't' of a certain species follows the differential equation

dPdt{{dP} \over {dt}} = 0.5P – 450. If P(0) = 850, then the time at which population becomes zero is :

Multiple Choice Options

  • A log⁡e18{\log _e}18
  • B 12log⁡e18{1 \over 2}{\log _e}18
  • C 2 log⁡e18{\log _e}18
  • D log⁡e9{\log _e}9

Step-by-Step Verified Solution

dpdt=p−9002{{dp} \over {dt}} = {{p - 900} \over 2}

∫8500dpp−900=∫0tdt2\int\limits_{850}^0 {{{dp} \over {p - 900}} = \int\limits_0^t {{{dt} \over 2}} }

⇒\Rightarrow ln⁡∣p−900∣8500=t2\ln |p - 900|_{850}^0 = {t \over 2}

⇒\Rightarrow ln⁡900−ln⁡50=t2\ln 900 - \ln 50 = {t \over 2}

⇒\Rightarrow t2=ln⁡18{t \over 2} = \ln 18

⇒t=2ln⁡18\Rightarrow t = 2\ln 18

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring