14. Find the accumulated present value of an investment over a 10 year period if there is a continuous money flow of $10,000 per year and the interest rate is 1.3% compounded continuously.
15. A company is considering expanding their production capabilities with a new machine that costs $52,000 and has a projected lifespan of 7 years. They estimate the increased production will provide a constant $8,000 per year of additional income. Money can earn 1.1% per year, compounded continuously. Should the company buy the machine?
a. Select an answer Yes, the present value of the machine is greater than the cost by No, the present value of the machine is less than the cost by
b. $ over the life of the machine
16. Find the present value of a continuous income stream F(t)=20+7t, where t is in years and F is in thousands of dollars per year, for 30 years, if money can earn 2.5% annual interest, compounded continuously.
Present value = thousand dollars.
17. Given f(x,y)=−2x^2+4xy^6+3y^5, find
fxx(x,y) =
fxy(x,y) =
18. Find the critical point of the function f(x,y)=−4−7x−5x^2+6y−2y^2
19. Suppose that f(x,y)=x^4+y^4−xy
Then the minimum is