Ex 9.3, 21 - Chapter 9 Class 12 Differential Equations

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Ex 9.3, 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 Principal = p Given, principa; increases at rate 5% per year ∴ 𝒅𝒑/𝒅𝒕 = 5% × p ∴ 𝑑𝑝/𝑑𝑡 = 5/100 × p 𝒅𝒑/𝒑 = 𝟏/𝟐𝟎 dt Integrating both sides ∫1▒𝑑𝑝/𝑝 = 1/20 ∫1▒𝑑𝑡 log p = 𝒕/𝟐𝟎 + log c log p − log c = 0.05t log 𝑝/𝑐 = 0.05t 𝒑/𝒄 = e0.05t Now, given that an amount of Rs 1000 is deposited with this bank Putting T = 0, P = 1000 in (1) 1000/𝐶= e0.05 × 0 1000/𝐶= e0 1000/𝐶= 1 𝒄= 1000 Now, we need to how much is the amount after 10 years So, Putting t = 10 & c = 1000 in (1) 𝑝/1000 = e0.05(10) 𝑝/1000 = 𝑒^0.5 𝑝/1000 = 1.648 p = 1648 ∴ The amount is Rs 1648 after 10 years.