Chapter 6.4, Problem 74E

Housing Starts: The Great Recession (Compare Exercise 88 in Section 6.2.) The Great Recession of 2007–2009 is largely attributed to the real estate crisis beginning in 2006, from which time the number of housing starts was approximately

$n\left(t\right)=2,400e^{-0.25t}-200\text{ thousand homes per year }\left(0\le t\le 4\right),$

where t is time in years since January 2006. Use the FTC to find an expression for the total number $N\left(T\right)$ of housing starts in the United States from January 2006 to time T. Hence estimate, to the nearest 0.1 million, the total number of housing starts from January 2006 through June 2009. (The actual number was around 4.9 million homes.) [HINT: Use the shortcuts.]