Using the derivative skill to answer the problem

You are going to buy a house at a purchase price of 200,000. The term t (in years) of a home mortgage at 7.5 % interest can be approximated by t = 13.375 In (x /(x-1250), x> 1250 where x is the monthly payment in dollars. A) Use a graphing utility to graph the model. B) Use the model to approximate the term of a home mortgage for which the monthly payment is $1398.43. What is the total amount paid? C) Use the model to approximate the term of a home mortgage for which the monthly payment is $1611.19. What is the total amount paid? D) Find the instantaneous rates of change of t with respect to x when x=$1398.43 and x= $1611.19. E) Write a short paragraph describing the benefit of the higher payment