Thread: differential equations modeling

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).
A(t) = 4500(1+0.04)^(t) - 5000t
dA/dt = 4500(1.04^t)ln(1.04) - 5000

Is that correct?

b) If A(0) = 10,000 how much money will be in the account in 5 years?

Sorry, not very close. You have neglected some features.

1) Initial balance. A(0) probably isn't zero. Note Part B.
2) Earnings and Expenses occur each year, not just once. You do have the expenses doing that, but not the income.

If you change just two things, it might be close, but perhaps only by luck. change your 4500 to A(0) and change 5000 to 500.

Give it some thought.