Housing Starts Housing starts in the United States can be approximated by...

Housing Starts Housing starts in the United States can be approximated by million homes per month (t ≥ 0) where t is time in months since January 2006.2 Numerically estimate limt→+∞ n(t) and interpret the answer. HINT [See Example 6.]

Example 6:

The percentage of U.S. Internet-connected households that have broadband connections can be modeled by

where t is time in years since 2000.*

Thus, in the long term (as t gets larger and larger), the percentage of U.S. Internet Tech Formula: connected households that have broadband is expected to approach 100%.

(Notice that in this case, we can simply put t = 0 to evaluate this limit.) Thus, the closer t gets to 0 (representing 2000) the closer P(t) gets to 8.475%, meaning that, in 2000, about 8.5% of Internet-connected households had broadband.