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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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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