Question

(1 point) John 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. John 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 2% per year (John can as his income goes up over time). _ save more (a) Set up a linear system of the form db mbm128, dt ds mabm228 dt 1m12 m = 1mn (b) Find b(t) and s(t) b(t) s(t)

Answer 1

9ouHon Considen he systen db STurtqu b)Soluc the Sgsten ab.04b+ ds 6 )6 02s wstte the mdeix fosm 0:02 he chreteisic equation o he Coebicteut metzot A is -A-2I0 O.04-7 0 02- O 004-)02-)0 therefose, he eigen values o metix A e 004,20.02- he einen veetoe o k medtix A ColFegponding to lki ergen vezos 0.04 wd 3= o'02 are espeeuely -50

the solttion o system s 0'04t 50 7 02E 002t Ge .02t Se al condiions b©)=500 SO)500 to find Constauls S(0) 500 566 L500 C2 Solve th equaiens, to qet C2500 G 5000 -500 Q5 500 the generd oluti on is O04 500 o' 02t 25500 25000 e bct) 255do e 6-02 500 e S=