a) Write a differential equation which models the rate of the change of the sum S(t) with t in years (this will involve the parameter k). S' = Note: Use S rather than S(t) since the latter confuses the computer. b) Use part a) to determine a formula for the sum S(t) -- (this will involve the parameter k): S(t) = c) What value of k will provide 2243000 dollars in 45 years? k =

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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A young person with no initial capital
invests k dollars per year in a retirement
account at an annual rate of return 0.06.
Assume that investments are made
continuously and that the return is compounded
continuously.
a) Write a differential equation which models the
rate of the change of the sum S(t) with t in
years (this will involve the parameter k).
S':
Note: Use S rather than S(t) since the latter
confuses the computer.
b) Use part a) to determine a formula for the
sum S(t) - (this will involve the parameter k):
S(t) =
%3D
c) What value of k will provide 2243000 dollars
in 45 years?
k =
Transcribed Image Text:A young person with no initial capital invests k dollars per year in a retirement account at an annual rate of return 0.06. Assume that investments are made continuously and that the return is compounded continuously. a) Write a differential equation which models the rate of the change of the sum S(t) with t in years (this will involve the parameter k). S': Note: Use S rather than S(t) since the latter confuses the computer. b) Use part a) to determine a formula for the sum S(t) - (this will involve the parameter k): S(t) = %3D c) What value of k will provide 2243000 dollars in 45 years? k =
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