Example 14 - In a bank, principal increases 5%. In how many

Example 14 - Chapter 9 Class 12 Differential Equations - Part 2
Example 14 - Chapter 9 Class 12 Differential Equations - Part 3
Example 14 - Chapter 9 Class 12 Differential Equations - Part 4
Example 14 - Chapter 9 Class 12 Differential Equations - Part 5

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

Transcript

Example 14 In a bank, principal increases continuously at the rate of 5% per year. In how many years Rs 1000 double itself ? Rate of change of principal = 5% of Principal 𝑑𝑃/𝑑𝑑 = 5% Γ— P 𝑑𝑃/𝑑𝑑 = 5/100 Γ— P 𝑑𝑃/𝑑𝑑 = 1/20 Γ— P 𝑑𝑝/𝑃 = 𝑑𝑑/20 Integrating both sides ∫1▒𝑑𝑝/𝑃 = ∫1▒𝑑𝑑/20 log |𝑃| = 𝑑/20 + C Removing log P = e^(𝑑/20 + 𝐢) Γ— ec P = e^(𝑑/20 + 𝐢) Γ— ec P = ke^(𝑑/20) where k = ec Now, we have to find in how many years Rs 1000 double it self Thus, we need to find time T when Principal is Rs 2000 First let us find k At t = 0, P = 1000 Putting in (1) P = ke^(𝑑/20) 1000 = ke^(0/20) 1000 = k e0 1000 = k Γ— 1 1000 = k So, k = 1000 Put k = 1000 in (1) P = ke^(𝑑/20) P = 1000 e^(𝑑/20) Now, we need to find time t when Principal is Rs 2000 Putting P = 2000, t = t 2000 = 1000 e^(𝑑/20) 2000/1000 = e^(𝑑/20) 2 = e^(𝑑/20) e^(𝑑/20) = 2 Taking log both sides log_𝑒⁑〖𝑒^(𝑑/20) γ€—=log_𝑒⁑2 t/20 log_𝑒⁑𝑒=log_𝑒⁑2 " " t/20Γ—1=log_𝑒⁑2 𝐭=𝟐𝟎 γ€–π’π’π’ˆγ€—_π’†β‘πŸ (log xπ‘Ž = π‘Žlog x) (log e = 1)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.