Chapter 4.5, Problem 81E

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Home Mortgage The term t (in years) of a $200,000 home mortgage at 7.5% interest can be approximated by t = − 13.375 ln x − 1250 x , 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 rate 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 monthly payment. (a) To determine To graph: The sketch of the model t=13.375lnx1250x,x>1250 where, x is the monthly payment in dollars and t is the term in years of a home mortgage of$200,000 at 7.5% interest.

Explanation

Given Information:

The model t=13.375lnx1250x,  x>1250 where x is the monthly payment in dollars and t is the term in years of a home mortgage of $200,000 at 7.5% interest. Graph: Consider the function t=13.375lnx1250x, x>1250. Steps to plot the graph of the function t=13.375lnx1250x using Ti 83 graphing utility: Step 1: Press “ON” button. Step2: Press “Y=” key on the graphing utility. Step3: Enter the function in the graphing utility as, “Y1=-13 (b) To determine To calculate: The term of a home mortgage at which the monthly payment is$1398.43 and also the total amount paid, if model is t=13.375lnx1250x,  x>1250 where x is the monthly payment in dollars and t is the term in years of a home mortgage of $200,000 at 7.5% interest. (c) To determine To calculate: The term of a home mortgage at which the monthly payment is$1611.19 and also the total amount paid, if model is t=13.375lnx1250x,  x>1250 where x is the monthly payment in dollars and t is the term in years of a home mortgage of $200,000 at 7.5% interest. (d) To determine To calculate: The instantaneous rate of change of t with respect to x, where x=$1398.43 and x=$1611.19, if the model is t=13.375lnx1250x, x>1250 where x is the monthly payment in dollars and t is the term in years of a home mortgage of$200,000 at 7.5% interest.

(e)

To determine

The benefit of the higher monthly payment in a paragraph, if the model is t=13.375lnx1250x,  x>1250 where x is the monthly payment in dollars and t is the term in years of a home mortgage of \$200,000 at 7.5% interest.

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