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(t) = 2,400e−0.25t − 200 thousand homes per year (0 ≤ t ≤ 4),
where t is time in years since January 2006.† Find an expression for the total number
N(t)
of housing starts in the United States from January 2006 to time t.
N(t) =

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.)
million homes