Broadband Access Pablo Pelogrande, a new summer intern at OHaganBooks.com in 2013, was asked by John O’Hagan to research the extent of broadband access in the United States. Pelogrande found some very old data online on broadband access from the start of 2001 to the end of 2003 and used it to construct the following quadratic model of the growth rate of broadband access:
n(t) = 2t2 − 6t + 12 million new American adults with broadband per year
(t is time in years; t = 0 represents the start 2000).
a. What is the appropriate domain of n?
b. According to the model, when was the growth rate at a minimum?
c. Does the model predict a zero growth rate at any particular time? If so, when?
d. What feature of the formula for this quadratic model indicates that the growth rate eventually increases?
e. Does the fact that n(t) decreases for t ≤ 1.5 suggest that the number of broadband users actually declined before June 2001? Explain.
f. Pelogande extrapolated the model in order to estimate the growth rate at the beginning of 2013 and 2014. What did he find? Comment on the answer.
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