# Application of a Differential Equation

• Oct 23rd 2011, 10:35 PM
antz215
Application of a Differential Equation
Hello I am looking for help on this question. Thanks in advance for looking :-)

A company wishes to set aside funds for future expansion and so arranges to make continuous deposits into a savings account at the rate of \$10,000 per year. The savings account earns 5% interest compounded continuously.

a) Set up the differential equation that is satisfied by the amount f(t) 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 5 years.

So I'm pretty sure for part a, the equation is y' = .05y + 10,000 ; y(0) = 0.
But I do not know what to do for part b. I do know that once you get the equation you will plug in 5 for t and get a dollar amount but that's all. Thanks in advance.
• Oct 23rd 2011, 10:54 PM
Prove It
Re: Application of a Differential Equation
Quote:

Originally Posted by antz215
Hello I am looking for help on this question. Thanks in advance for looking :-)

A company wishes to set aside funds for future expansion and so arranges to make continuous deposits into a savings account at the rate of \$10,000 per year. The savings account earns 5% interest compounded continuously.

a) Set up the differential equation that is satisfied by the amount f(t) 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 5 years.

So I'm pretty sure for part a, the equation is y' = .05y + 10,000 ; y(0) = 0.
But I do not know what to do for part b. I do know that once you get the equation you will plug in 5 for t and get a dollar amount but that's all. Thanks in advance.

How can you substitute a value for t into the differential equation when you don't know what function of t that y is?

Solving the differential equation enables you to find this function y.

I suggest you look up "First Order Linear Ordinary Differential Equations".