Peter opens a bank account with an initial balance of 2000 dollars. Letb(t)be the balance in the account at timet. Thusb(0)=2000. The bank is paying interest at a continuous rate of 6% per year. Peter makes deposits into the account at a continuous rate ofs(t)dollars per year. Suppose thats(0)=800 and thats(t)is increasing at a continuous rate of 3% per year (Peter can save more as his income goes up over time).

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

db/dt=m11b+m12s,

ds/dt=m21b+m22s.

m11=? m12=? m21=? m22=?

find b(t) and s(t)