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

Transcript

Ex 9.4, 21 In a bank, principal increases continuously at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank , how much will it worth after 10 years (๐‘’^0.5=1.648) Let Principle = p Given, principle increases at rate 5% per year โˆด ๐‘‘๐‘/๐‘‘๐‘ก = 5% ร— p โˆด ๐‘‘๐‘/๐‘‘๐‘ก = 5/100 ร— p ๐‘‘๐‘/๐‘ = 1/20 dt Integrating both sides โˆซ1โ–’๐‘‘๐‘/๐‘ = 1/20 โˆซ1โ–’๐‘‘๐‘ก log p = ๐‘ก/20 + log c log p โˆ’ log c = 0.05t log ๐‘/๐‘ = 0.05t ๐‘/๐‘ = e0.05t Now, given that an amount of Rs 1000 is deposited with this bank Putting T = 0, P = 1000 in (1) 1000/๐ถ= e0.05 ร— 0 1000/๐ถ= e0 1000/๐ถ= 1 ๐‘= 1000 โ€ฆ(1) Now, we need to how much is the amount after 10 years So, Putting t = 10 & c = 1000 in (1) ๐‘/1000 = e0.05(10) ๐‘/1000 = ๐‘’^0.5 ๐‘/1000 = 1.648 p = 1648 โˆด The amount is Rs 1648 after 10 years. (Given e0.5 = 1.648)

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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.