Modeling Bank Account Growth with Differential Equations

[lordy12]

1. You have a bank account that earns 4% interest per year. You earn $4500 per year designing web pages for local businesses and spend $5000 buying CD's and computer games.
a.) Find differential equation that models account t years from now, A(t). b) If A(0) = 10,000 how much money will be in the account in 5 years?

Homework Equations

3. a. dA/dt = 4500t - 5000t b. 10000(1.04)^5 + 4500*5 - 5000*5. Is this correct? The problem for part b is that I can't use a calculator and the problem gives me a hint that e^(1/5) = 6/5/

 

[cristo]

You've not used the 4% interest yet though. That says that every year 4% of your money will be added on. Can you add this into the differential equations?