   Chapter 5.4, Problem 79E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

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

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Mortgage Debt The rate of change of mortgage debt outstanding for one- to four-family homes in the United States from 2000 through 2013 can be modeled by d M d t = − 1.079   +   2.555 t 0.5 −   0.75428 t   +   0.0000061 e t d t where M is the mortgage debt outstanding (in trillions of dollars) and t is the year, with t = 0 corresponding to 2000. In 2000, the mortgage debt outstanding in the United States was \$5.1 trillion. (Source: Board of Governors of the Federal Reserve System)(a) Write a model for the debt as a function of t.(b) What was the average mortgage debt outstanding for 2000 through 2013?

(a)

To determine

To calculate: A model for the debt as a function of t with t=0 corresponding to 2000, where rate of change of mortgage debt outstanding for one to four family homes from 2000 to 2013 is modeled by the function,

dMdt=1.079+2.5550t0.50.75428t+0.0000061et,

Where M is the mortgage debt outstanding and t is the year.

Explanation

Given Information:

The rate of change of mortgage debt outstanding for one to four family homes in the United States from 2000 to 2013 is modeled by the function,

dMdt=1.079+2.5550t0.50.75428t+0.0000061et,

Where M is the mortgage debt outstanding and t is the year and also the mortgage debt outstanding was 5.1 trillion in the year 2000.

Calculation:

Consider the model,

dMdt=1.079+2.5550t0.50.75428t+0.0000061et

In order to determine a model for the debt as a function of t, integrate the provided model with respect to t as,

M(t)=(1.079+2.5550t0.50.75428t+0.0000061et)dt=1.079t+2.55501.5t1.50.754282t2+0.0000061et+C=1

(b)

To determine

To calculate: The average mortgage debt outstanding for 2000 through 2013 where rate of change of mortgage debt outstanding for one to four family homes from 2000 to 2013 is modeled by the function,

dMdt=1.079+2.5550t0.50.75428t+0.0000061et,

Where M is the mortgage debt outstanding and t is the year.

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