Check sibling questions

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

Get live Maths 1-on-1 Classs - Class 6 to 12


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)

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.