   Chapter 11.5, Problem 104E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Subprime Mortgage Debt during the Housing Bubble During the real estate run-up in 2000–2008 the value of subprime (normally classified as risky) mortgage debt out- standing in the United States was approximately A ( t ) = 1.350 1 + 4.2 e − 0.53 t  percent ( 0 ≤ t ≤ 8 ) t years after the start of 2000.56Subprime debt outstanding How fast, to the nearest \$1 billion, was subprime mortgage debt increasing at the start of 2005? How would you check that the answer is approximately correct by looking at the graph? [HINT: See Example 3.]

To determine

To calculate: The rate at which the mortgage debt increased at the start of 2005 if the value of mortgage debt outstanding is given by the equation A(t)=13501+4.2e0.53t billion dollars (0t8) t years after the start of 2000 and to check if the answer is correct with the help of the given graph.

Explanation

Given Information:

The value of mortgage debt outstanding is given by the equation A(t)=13501+4.2e0.53t billion dollars (0t8) t years after the start of 2000. The graph is as follows:

Formula used:

The following derivative formula is used:

ddx(ex)=ex

Calculation:

Consider that value of mortgage debt outstanding is given by the equation A(t)=13501+4.2e0.53t billion dollars (0t8) t years after the start of 2000.

Re-write A(t)=13501+4.2e0.53t billion dollars as A(t)=1350(1+4.2e0.53t)1

The rate of change of A(t) is equal to the rate of increase of mortgage debt.

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