3. Mortgage Payment Problem: People who buy houses usually get a loan to pay for most of the house and pay on the resulting mortgage each month. Suppose you get a $50,000 loan and pay it back at $550.34 per month with an interest rate of 12% per year (1% per month). Your balance, dollars, after n monthly payments is given by the algebraic equation B 50,000( 1.01") + 55034 (1-1.01") 0.01 a. Make a table of your balances at the end of each 12 months for the first 10 years of the mortgage. To save time, use the table feature of your calculator to do this. b. How many months will it take you to pay off the entire mortgage? Show how you get your answer. Plot on your calculator the graph of Bas a function of n from -0 until the mortgage is paid off. Sketch the graph below. C. d. True or False: "After half the payments have been made, half the original balance remains to be paid." Show that your conclusion agrees with your graph from part c. e. Give the domain and range of this function. Explain why the domain contains only integers