John opens a bank account with an initial balance of 1500 dollars. Let $b(t)$ be the balance in the account at time $t$. Thus $b(0)=1500$. The bank is paying interest at a continuous rate of 3% per year. John makes deposits into the account at a continuous rate of $s(t)$ dollars per year. Suppose that $s(0)=1300$ and that $s(t)$ is increasing at a continuous rate of 6% per year (John can save more as his income goes up over time).

(a) Set up a linear system of the form $$\begin{array}{rcl} \displaystyle \frac{db}{dt} & = & m_{11} b + m_{12} s, \cr & & \cr \displaystyle \frac{ds}{dt} & = & m_{21} b + m_{22} s. \end{array}$$
$m_{11} =$ ,
$m_{12} =$ ,
$m_{21} =$ ,
$m_{22} =$ .

(b) Find $b(t)$ and $s(t)$.
$b(t)=$ ,
$s(t)=$ .