A person planning for her retirement arranges to make continuous deposits into a savings account at the rate of $3400 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 16 years. (a) y' = 100* 5y+3400 (Type an expression using y as the variable.) (b) f(t) = 85000
A person planning for her retirement arranges to make continuous deposits into a savings account at the rate of $3400 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 16 years. (a) y' = 100* 5y+3400 (Type an expression using y as the variable.) (b) f(t) = 85000
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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![A person planning for her retirement arranges to make continuous deposits into a savings account at the rate of $3400 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 16 years.
4
(a) y' =
-y+ 3400
100
%3D
(Type an expression using y as the variable.)
t
(b) f(t) = 85000
25
- 1
There will be $
in the account at the end of 16 years.
(Round to the nearest integer as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06e5b72a-2f26-4603-b5c0-7037b02ca80a%2Fab83b38e-919c-4e96-81ff-7baa21bc4fab%2Fkezt02_processed.png&w=3840&q=75)
Transcribed Image Text:A person planning for her retirement arranges to make continuous deposits into a savings account at the rate of $3400 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 16 years.
4
(a) y' =
-y+ 3400
100
%3D
(Type an expression using y as the variable.)
t
(b) f(t) = 85000
25
- 1
There will be $
in the account at the end of 16 years.
(Round to the nearest integer as needed.)
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