Ex 9.4, 21 - Chapter 9 Class 12 Differential Equations

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 𝑒﷮0.5﷯=1.648﷯ Let Principle = p Given, principle increases at rate 5% per year ∴ 𝑑𝑝﷮𝑑𝑡﷯ = 5% × P ∴ 𝑑𝑝﷮𝑑𝑡﷯ = 5﷮100﷯ × p 𝑑𝑝﷮𝑝﷯ = 1﷮20﷯ dt Integrating both sides ﷮﷮ 𝑑𝑝﷮𝑝﷯﷯ = 1﷮20﷯ ﷮﷮𝑑𝑡﷯ log p = 𝑡﷮20﷯ + log c log p − log c = 0.05t log 𝑝﷮𝑐﷯ = 0.05t 𝑝﷮𝑐﷯ = e0.05t At T = 0, P = 1000 100﷮𝐶﷯= e0.05t 100﷮𝐶﷯= e0 100﷮𝐶﷯= 1 𝑐= 1000 Now, we need to find P at t = 10 years Putting t = 10 & c = 1000 value in (1) 𝑝﷮1000﷯ = e0.05(10) 𝑝﷮1000﷯ = 𝑒﷮0.5﷯ 𝑝﷮1000﷯ = 1.648 P = 1648 ∴ The principal is Rs 1648 after 10 years.