   Chapter 11.5, Problem 103E 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 Mortgages during the Housing Bubble During the real estate run-up in 2000–2008 the percentage of mortgages issued in the United States that were subprime (normally classified as risky) could be approximated by A ( t ) = 15.0 1 + 8.6 e − 0.59 t  percent ( 0 ≤ t ≤ 8 ) t years after the start of 2000.55Subprime mortgages How fast, to the nearest 0.1%, was the percentage increasing at the start of 2003? How would you check that the answer is approximately correct by looking at the graph? [HINT: See Example 3.]

To determine

To calculate: The increase of mortgages at the start of 2003 if the percentage of mortgages issued that were risky is given by the equation A(t)=151+8.6e0.59t percent (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 percentage of mortgages issued that were risky is given by the equation A(t)=151+8.6e0.59t percent (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 percentage of mortgages issued that were risky is given by the equation A(t)=151+8.6e0.59t percent (0t8) t years after the start of 2000.

Re-write A(t)=151+8.6e0.59t percent as A(t)=15(1+8.6e0.59t)1

The rate of change of A(t) is equal to the rate of change of the percentage.

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