Ngozi opens a bank account w i t h an initial balance of 1,000 Nigerian naira. Let b(t)

Chapter 9, Problem 21

(choose chapter or problem)

Ngozi opens a bank account w i t h an initial balance of 1,000 Nigerian naira. Let b(t) be the balance in the account at time r; we are told that /?(0) = 1,000. The bank is paying interest at a continuous rate of 5% per year. Ngozi makes deposits into the account at a continuous rate of s (t) (measured in naira per year). We are told that 5(0) = 1,000 and that s(t) is increasing at a c o n t i n u o u s rate of 7% per year. (Ngozi can save more as her income goes up over time.) a. Set up a linear system of the formdb dtds dt= !b +Is = !b +Is(Time is measured in years.) b. Find b(t) and s(t).