David opens a bank account with an initial balance of 500 dollars. Let b(t) be the balance in the account at time t. Thus b(0) = 500. The bank is paying interest at a continuous rate of 4% per year. David makes deposits into the account at a continuous rate of s(t) dollars per year. Suppose that s(0) = 500 and that s(t) is increasing at a continuous rate of 5% per year (David can save more as his income goes up over time). (a) Set up a linear system of the form dh mub+ m128, dt ds = myb + m2s. dt mi1 = m12 = m21 = m22 = (b) Find b(t) and s(t). b(t) = s(t) =

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