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A person planning for her retirement arranges to make continuous deposits into a savings account at the rate of $3000 per year. The savings account earns 4% interest compounded continuously. (a) Set up a differential equation that is satisfied by f(0), the amount of money in the account at time t. (b) Solve the differential equation in part (a), assuming that f(0) = 0, and determine how much money will be in the account at the end of 26 years. (a) y' =O (Type an expression using y as the variable.) (b) () = D There will be s in the account at the end of 26 years. (Round to the nearest integer as needed.)

A person planning for her retirement arranges to make continuous deposits into a savings account at the rate of $3000 per year. The savings account earns 4% interest compounded continuously. (a) Set up a differential equation that is satisfied by f(0), the amount of money in the account at time t. (b) Solve the differential equation in part (a), assuming that f(0) = 0, and determine how much money will be in the account at the end of 26 years. (a) y' =O (Type an expression using y as the variable.) (b) () = D There will be s in the account at the end of 26 years. (Round to the nearest integer as needed.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A person planning for her retirement arranges to make continuous deposits into a savings account at the rate of $3000 per year. The savings account earns 4% interest compounded continuously. (a) Set up a differential equation that is satisfied by f(t), the amount of money in the account at time t. (b) Solve the differential equation in part (a), assuming that f(0) = 0, and determine how much money will be in the account at the end of 26 years. %3D (a) y' = (Type an expression using y as the variable.) (b) f(t) = There will be $ in the account at the end of 26 years. (Round to the nearest integer as needed.)
Transcribed Image Text:A person planning for her retirement arranges to make continuous deposits into a savings account at the rate of $3000 per year. The savings account earns 4% interest compounded continuously. (a) Set up a differential equation that is satisfied by f(t), the amount of money in the account at time t. (b) Solve the differential equation in part (a), assuming that f(0) = 0, and determine how much money will be in the account at the end of 26 years. %3D (a) y' = (Type an expression using y as the variable.) (b) f(t) = There will be $ in the account at the end of 26 years. (Round to the nearest integer as needed.)
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