A study prepared for the National Association of Realtors estimated that the number of housing starts per year over the next 5 years will be N(r) =
7
1 + 0.02r 2
million units, where r (percent) is the mortgage rate. Suppose the mortgage rate t months from now will be
r(t) =
5t + 75
t + 10
(0 ≤ t ≤ 24)
percent/year.
(a) Find an expression for the number of housing starts per year as a function of t, t months from now.