Ex 9.3

Chapter 9 Class 12 Differential Equations
Serial order wise

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### Transcript

Ex 9.3, 20 In a bank, principal increases continuously at the rate of ๐% per year. Find the value of r if Rs 100 double itself in 10 years (logโกใ2=0.6931ใ ) Let Principle = p Given, principle increases ar rate r % per year โด ๐๐/๐๐ก = ๐ % ร P โด ๐๐/๐๐ก = ๐/100 ร p ๐๐/๐ = ๐/100 dt Integrating both sides โซ1โ๐๐/๐ = ๐/100 โซ1โ๐๐ก log p = ๐๐ก/100 + log c log p โ log c = ๐๐ก/100 log ๐/๐ = ๐๐ก/100 ๐/๐ = ๐^(๐๐ก/100) As we have put Rs 100 initially Putting t = 0 and p = 100 in (1) 100/๐ = ๐^((๐ ร 0)/100) 100/๐ = e^0 100/๐ = 1 c = 100 โฆ(1) Putting value of C in equation (1) ๐/(100 ) = e^(๐๐ก/100) Also, given that Rs 100 will double itself in 10 years โด Putting t = 10, p = 200 in the equation 200/(100 ) = e^(10๐/100) 2 = e^(๐/10) log 2 = ๐/10 0.6931 = ๐/10 r = 6.931 โด Rate of interest = r = 6.931 %

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.