Chapter 4.5, Problem 106E

Subprime Mortgage Debt during the Housing Bubble (Compare Exercise 104.) During the real estate run-up in 2000–2008 the value of subprime (normally classified as risky) mortgage debt outstanding in the United States could be approximated by

$A\left(t\right)=\frac{1,350x}{1+4.2{\left(1.7\right)}^{-t}}\text{ percent}\left(0\le t\le 8\right)$

t years after the start of 2000.⁵⁸

a. How fast, to the nearest 1%.was the percentage increasing at the start of 2005?

b. Compute ${\lim }_{t\to +\infty }A\left(t\right)$

and ${\lim }_{t\to +\infty }A\text{'}\left(t\right)$. What do the answers tell you about subprime mortgages?