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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.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo