# Misc 15 - Chapter 9 Class 12 Differential Equations

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc 15 The population of a village increases continuously at the rate proportional to the number of its inhabitants present at any time. If the population of the village was 20,000 in 1999 and 25000 in the year 2004 , what will be the population of the village in 2009 ? Let y be the population at time t Given : 𝑑𝑦𝑑𝑡 ∝ y 𝑑𝑦𝑑𝑡 = ky 𝑑𝑦𝑦 = kdt Integrating both sides 𝑑𝑦𝑦=𝑘 𝑑𝑡 log y = Kt + C In 1999, t = 0 & y = 20000 log 20000 = k(0) + C C = log 2000 Put value in (1) log y = kt + c log y = kt + log 20000 In 2004, t = 5 &y = 25000 Putting values in (2) log 25000 = 5k + log 20000 log 25000 − log 20000 = 5k log 2500020000 = 5k 15 log 54 = k k = 15 log 54 Put value of k in (2) log y = kt + log 20000 log y = 𝑡5 log 54 + log 20000 Now, In 2009, t = 10 , we need to find value of y Putting t = 10 in (3) log 𝑦 = 105 log 54 + log 20000 log y − log 20000 = 2 log 54 log 𝑦20000 = log 52 42 log 𝑦20000 = log 2516 Removing log 𝑦20000 = 2516 y = 2516×20000 y = 31250 ∴ Population of village in 2009 is 31250

Chapter 9 Class 12 Differential Equations

Serial order wise

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.