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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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BuyFindarrow_forward

Finite Mathematics and Applied Cal...

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

Subprime Mortgages during the Housing Crisis (Com- pare Exercise 29 in Section 10.4.) The percentage of mort- gages issued in the United States during the period 2000–2009 that were subprime (normally classified as risky) can be approximated by

A ( t ) = 15 1 + 8.6 ( 1.8 ) t ( 0 t 9 ) , where t is the number of years since the start of 2000.

a. Estimate A ( 6 )  and  A ' ( 6 ) . (Round answers to two significant digits.) What do the answers tell you about subprime mortgages?

b. Graph the extrapolated function and its derivative for 0 t 16 , and use your graphs to describe how the derivative behaves as t becomes large. (Express this behavior in terms of limits if you have studied the sections on limits.) What does this tell you about sub- prime mortgages? [HINT: See Example 5.]

(a)

To determine

To calculate: The value of A(6) and A(6) then explain it where A(t) represents the number of mortgages that were subprime in 200009 by U.S. The function is A(t)=151+8.6(1.8)t and 0t9 here t is number of years after 2000.

Explanation

Given information:

The expression A(t)=151+8.6(1.8)t, which represents the number of mortgages that were subprime in 200009 by U.S. and 0t9 here t is number of years after 2000.

Formula used:

The instantaneous rate of change is the derivative of the function.

The balance difference quotient of a function f(x) at any point a is f(a)f(a+h)f(ah)2h

Calculation:

Consider the expression A(t)=151+8.6(1.8)t that represents the number of mortgages that were subprime in 200009

Substitute, 6 for t in A(t)=151+8.6(1.8)t

A(6)=151+8.6(1.8)612.0

Substitute, 6 for a, 0.0001 for h in f(a)f(a+h)f(ah)2h

A(6)A(6+0.001)A(60.0001)2(0.0001)A(6

(b)

To determine

To graph: The function A(t)=151+8.6(1.8)t and its derivative in range 0t16 which represents the number of mortgages that were subprime in 200009 by U.S. and 0t9 here t is number of years after 2000 also interpret the derivative of the graph for large t in terms of limit and explain it.

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Chapter 10 Solutions

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Sect-10.1 P-11ESect-10.1 P-12ESect-10.1 P-13ESect-10.1 P-14ESect-10.1 P-15ESect-10.1 P-16ESect-10.1 P-17ESect-10.1 P-18ESect-10.1 P-19ESect-10.1 P-20ESect-10.1 P-21ESect-10.1 P-22ESect-10.1 P-23ESect-10.1 P-24ESect-10.1 P-25ESect-10.1 P-26ESect-10.1 P-27ESect-10.1 P-28ESect-10.1 P-29ESect-10.1 P-30ESect-10.1 P-31ESect-10.1 P-32ESect-10.1 P-33ESect-10.1 P-34ESect-10.1 P-35ESect-10.1 P-36ESect-10.1 P-37ESect-10.1 P-38ESect-10.1 P-39ESect-10.1 P-40ESect-10.1 P-41ESect-10.1 P-42ESect-10.1 P-43ESect-10.1 P-44ESect-10.1 P-45ESect-10.1 P-46ESect-10.1 P-47ESect-10.1 P-48ESect-10.1 P-49ESect-10.1 P-50ESect-10.1 P-51ESect-10.1 P-52ESect-10.1 P-53ESect-10.1 P-54ESect-10.1 P-55ESect-10.1 P-56ESect-10.1 P-57ESect-10.1 P-58ESect-10.1 P-59ESect-10.1 P-60ESect-10.1 P-61ESect-10.1 P-62ESect-10.1 P-63ESect-10.1 P-64ESect-10.1 P-65ESect-10.1 P-66ESect-10.1 P-67ESect-10.1 P-68ESect-10.1 P-69ESect-10.1 P-70ESect-10.1 P-71ESect-10.1 P-72ESect-10.1 P-73ESect-10.1 P-74ESect-10.2 P-1ESect-10.2 P-2ESect-10.2 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