Slide3.JPG

Slide5.JPG
Slide6.JPG Slide7.JPG Slide8.JPG

  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise

Transcript

Example 14 In a bank, principal increases continuously at the rate of 5% per year. In how many years Rs 1000 double itself ? Rate of change of principal = 5% of Principal ๐‘‘๐‘ƒ/๐‘‘๐‘ก = 5% ร— P ๐‘‘๐‘ƒ/๐‘‘๐‘ก = 5/100 ร— P ๐‘‘๐‘ƒ/๐‘‘๐‘ก = 1/20 ร— P ๐‘‘๐‘/๐‘ƒ = ๐‘‘๐‘ก/20 Integrating both sides โˆซ1โ–’๐‘‘๐‘/๐‘ƒ = โˆซ1โ–’๐‘‘๐‘ก/20 log |๐‘ƒ| = ๐‘ก/20 + C Removing log P = e^(๐‘ก/20 + ๐ถ) ร— ec P = e^(๐‘ก/20 + ๐ถ) ร— ec P = ke^(๐‘ก/20) where k = ec Now, we have to find in how many years Rs 1000 double it self Thus, we need to find time T when Principal is Rs 2000 First let us find k At t = 0, P = 1000 Putting in (1) P = ke^(๐‘ก/20) 1000 = ke^(0/20) 1000 = k e0 1000 = k ร— 1 1000 = k So, k = 1000 Put k = 1000 in (1) P = ke^(๐‘ก/20) P = 1000 e^(๐‘ก/20) Now, we need to find time t when Principal is Rs 2000 Putting P = 2000, t = t 2000 = 1000 e^(๐‘ก/20) 2000/1000 = e^(๐‘ก/20) 2 = e^(๐‘ก/20) e^(๐‘ก/20) = 2 Taking log both sides log_๐‘’โกใ€–๐‘’^(๐‘ก/20) ใ€—=log_๐‘’โก2 t/20 log_๐‘’โก๐‘’=log_๐‘’โก2 " " t/20ร—1=log_๐‘’โก2 ๐ญ=๐Ÿ๐ŸŽ ใ€–๐’๐’๐’ˆใ€—_๐’†โก๐Ÿ (log x๐‘Ž = ๐‘Žlog x) (log e = 1)

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.