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
where t is the number of years since the start of 2000.
a. Estimate . (Round answers to two significant digits.) What do the answers tell you about subprime mortgages?
b. Graph the extrapolated function and its derivative for , 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.]
To calculate: The value of and then explain it where represents the number of mortgages that were subprime in by U.S. The function is and here t is number of years after .
The expression , which represents the number of mortgages that were subprime in by U.S. and here t is number of years after .
The instantaneous rate of change is the derivative of the function.
The balance difference quotient of a function at any point a is
Consider the expression that represents the number of mortgages that were subprime in
Substitute, for in
Substitute, for , for in
To graph: The function and its derivative in range which represents the number of mortgages that were subprime in by U.S. and here t is number of years after also interpret the derivative of the graph for large t in terms of limit and explain it.
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