Economic Growth The value of sold goods in Mexico can be approximated by...

Economic Growth The value of sold goods in Mexico can be approximated by

Where t is time in months since January 2005. Numerically estimate limt→+∞ v(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.*

a. Estimate limt→+∞ P(t) and interpret the answer.

b. Estimate limt→0+ P(t) and interpret the answer.

Solution

a. Figure 8 shows a plot of P(t) for 0 ≤ t ≤ 20.

Using either the numerical or the graphical approach, we find

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