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

Transcript

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
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.