MATH1326-THQ10(solution.pdf

Intends to make continuous deposits at the rate of

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intends to make continuous deposits at the rate of $1,400 a year until she retires. How much will she has accumulated at that time ? ?𝐴 ?𝑡 = 𝑟𝐴 + ?, 𝑟 = 0.02, ? = 1400, 𝐴(0) = 𝐴 0 = 75000 Method #1: Separable Method #2: Integrating Factor ?𝐴 𝑟𝐴 + ? = ?𝑡 ⇒ ?𝑛|𝑟𝐴 + ?| = 𝑟𝑡 + ? ⇒ 𝑟𝐴 + ? = ?? 𝑟𝑡 ⇒ 𝐴 = 𝑀? 𝑟𝑡 ? 𝑟 , 𝑀 = ? 𝑟 ?𝐴 ?𝑡 − 𝑟𝐴 = ? ⇒ 𝐼(?) = ? ∫ −𝑟𝑑𝑡 = ? −𝑟𝑡 ⇒ ? −𝑟𝑡 ?𝐴 ?𝑡 − ? −𝑟𝑡 𝑟𝐴 = ? −𝑟𝑡 ? ⇒ ? 𝑥 (? −𝑟𝑡 𝐴) = ? −𝑟𝑡 ? ⇒ ? −𝑟𝑡 𝐴 = ∫ ? −𝑟𝑡 ? ?𝑡 ⇒ ? −𝑟𝑡 𝐴 = − 𝐷 𝑟 ? −𝑟𝑡 + 𝑀 , ⇒ 𝐴 = 𝑀? 𝑟𝑡 ? 𝑟 , But 𝐴(0) = 𝑀 − 𝐷 𝑟 = 𝐴 0 => 𝑀 = 𝐴 0 + 𝐷 𝑟 , ⇒ 𝐴 = (𝐴 0 + ? 𝑟 )? 𝑟𝑡 ? 𝑟 ⇒ 𝐴 = (75000 + 1400 0.02 )? 0.02𝑡 1400 0.02 ⇒ 𝐴 = 145000? 0.02𝑡 − 70000 ⇒ 𝐴(25) = 145000? 0.02(25) − 70000 ≈ $169065
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