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Ex 9.4, 20 - In a bank, principal increases continuously at r%

Ex 9.4, 20 - Chapter 9 Class 12 Differential Equations - Part 2
Ex 9.4, 20 - Chapter 9 Class 12 Differential Equations - Part 3

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Ex 9.4, 20 In a bank, principal increases continuously at the rate of ๐‘Ÿ% 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 โˆด ๐‘‘๐‘/๐‘‘๐‘ก = ๐‘Ÿ % ร— P โˆด ๐‘‘๐‘/๐‘‘๐‘ก = ๐‘Ÿ/100 ร— p ๐‘‘๐‘/๐‘ = ๐‘Ÿ/100 dt Integrating both sides โˆซ1โ–’๐‘‘๐‘/๐‘ = ๐‘Ÿ/100 โˆซ1โ–’๐‘‘๐‘ก log p = ๐‘Ÿ๐‘ก/100 + log c log p โˆ’ log c = ๐‘Ÿ๐‘ก/100 log ๐‘/๐‘ = ๐‘Ÿ๐‘ก/100 ๐‘/๐‘ = ๐‘’^(๐‘Ÿ๐‘ก/100) As we have put Rs 100 initially Putting t = 0 and p = 100 in (1) 100/๐‘ = ๐‘’^((๐‘Ÿ 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‘Ÿ๐‘ก/100) Also, given that Rs 100 will double itself in 10 years โˆด Putting t = 10, p = 200 in the equation 200/(100 ) = e^(10๐‘Ÿ/100) 2 = e^(๐‘Ÿ/10) log 2 = ๐‘Ÿ/10 0.6931 = ๐‘Ÿ/10 r = 6.931 โˆด Rate of interest = r = 6.931 %

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.