$(1$ point$)$ John opens a bank account with an initial balance of $1000$ dollars. Let $b(t)$ be the balance in the account at time $t.$ Thus $b(0)=1000.$ The bank is paying interest at a continuous rate of $6\%$ per year. John makes deposits into the account at a continuous rate of $s(t)$ dollars per year. Suppose that $s(0)=900$ and that $s(t)$ is increasing at a continuous rate of $3\%$ per year $($John can save more as his income goes up over time$).$

$($a$)$ Set up a linear system of the form

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

$b(t)=$

$s(t)=$