Liam opens a bank account with an initial balance of $2000$ dollars. Let $b(t)$ be the balance in the account at time $t$. Thus $b(0)=2000$. The bank is paying interest at a continuous rate of $3\%$ per year. Liam makes deposits into the account at a continuous rate of $s(t)$ dollars per year. Suppose that $s(0)=1900$ and that $s(t)$ is increasing at a continuous rate of $5\%$ per year (Liam can save more as his income goes up over time). Set up a linear system of the form $$\frac{db}{dt}=m_{11}b+m_{12}s\\ \frac{ds}{dt}=m_{21}b+m_{22}s$$ Find the coefficients $m_x$ and find $b(t)$ and $s(t)$.
I thought this was quite straight forward,
$$\frac{db}{dt}=2000b+2000\cdot0.03s$$ $$\frac{ds}{dt}=1900b+0.05\cdot 1900 s$$
but it is not. If the interest is built on the initial input, $2000$, then wouldn't this be right?