2. An investor has an investment opportunity that pays an annual interest rate of r>0. Investing x dollars for T years will lead to a balance of f(x;r,T)=xerT dollars. (a) If r=0.05, how much money should be invested to have 10,000 dollars after T=10 years? (b) If r=0.05, how many years will it take for the investor to double her money? (c) After investing x dollars at an annual interest rate of r>0, how many years will it take for the investor to have a balance of B dollars? Assume that B>x. Solve for T in terms of r and call your solution T(r;x,B). Show that the solution T(r;x,B) is decreasing. What is the economic interpretation of this result? 2. An investor has an investment opportunity that pays an annual interest rate of r>0. Investing x dollars for T years will lead to a balance of f(x;r,T)=xerT dollars. (a) If r=0.05, how much money should be invested to have 10,000 dollars after T=10 years? (b) If r=0.05, how many years will it take for the investor to double her money? (c) After investing x dollars at an annual interest rate of r>0, how many years will it take for the investor to have a balance of B dollars? Assume that B>x. Solve for T in terms of r and call your solution T(r;x,B). Show that the solution T(r;x,B) is decreasing. What is the economic interpretation of this result