*B(t)*is the unpaid balance and

*B'(t) = 0.02B-400*.

What is the most you can borrow without going further into debt each month?**Solution**: We can calculate that

\(\displaystyle B(t) = B_0e^{0.02t}+20000\).

I need to find B_0 so that B'(t) is not increasing, or \(\displaystyle B'(t) <= 0\).

\(\displaystyle B'(t) = 0.02\left(B_0e^{0.02t}+20000\right)-400 = 0.02 B_0e^{0.02t}\)

But that last expression is always positive (assuming I borrowed a positive amount of money).