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Ex 9.4

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Chapter 9 Class 12 Differential Equations

Serial order wise

Last updated at Dec. 10, 2019 by Teachoo

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Ex 9.4, 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 (logโกใ2=0.6931ใ ) Let Principle = p Given, principle increases ar rate r % per year โด ๐๐/๐๐ก = ๐ % ร P โด ๐๐/๐๐ก = ๐/100 ร p ๐๐/๐ = ๐/100 dt Integrating both sides โซ1โ๐๐/๐ = ๐/100 โซ1โ๐๐ก log p = ๐๐ก/100 + log c log p โ log c = ๐๐ก/100 log ๐/๐ = ๐๐ก/100 ๐/๐ = ๐^(๐๐ก/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 โฆ(1) Putting value of C in equation (1) ๐/(100 ) = e^(๐๐ก/100) Also, given that Rs 100 will double itself in 10 years โด 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 โด Rate of interest = r = 6.931 %