Chapter 12.4, Problem 42E

Subprime Mortgage Debt during the Housing Bubble During the real estate run-up in 2000–2008 the value of sub- prime (normally classified as risky) mortgage debt outstanding in the United States was approximately

$A\left(t\right)=\frac{1,350}{1+4.2{\left(1.7\right)}^{-t}}\text{ billion dollars }\left(0\le t\le 8\right)$ t years after the start of 2000. Graph the derivative $A\text{'}\left(t\right)\text{ of }A\left(t\right)$ usingan extended domain of $0\le t\le 15$. Determine the approximate coordinates of the maximum, and determine the behavior of $A\text{'}\left(t\right)$ atinfinity. What do the answers tell you?