7. Recall that with continuous compounding at an interest rate of > >. 0, an investment / (?) withinitial investment in = /(0) is 1(t) = Inert. What happens If you wish to withdraw funds from the investment at a rate of spending S', where S' > U is constant? The differential equation is Your goals are as follow. You have an inivel investment , and you cannot change it or the rate ". You want to be able to suend as much as possible but you also don't want to ever spend ail your money. What amount of spending rate S can you hear? Hint: If you're not sure what to do, find and classify the equilibria in this model and think about which initial conditions lead towhich long-term behaviors. O Make sure S C . ( Any S. > 0 will lead to eventual loss of all funds. O Make sure S S r. Make care 5 3 +70 O Make sure Sip