Question

Pablo Pelogrande, a new summer intern at OHaganBooks.com in 2015, 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? (Enter your answer using interval notation.) (b) According to the model, when was the growth rate at a minimum? The growth rate was at a minimum at t = , midway through ---Select--- . (c) Does the model predict a zero growth rate at any particular time? If so, when? Yes, the model has a zero growth rate before 2000. Yes, the model has a zero growth rate after 2003. Yes, the model has a zero growth rate at the minimum. No, the model does not have a zero growth rate. (d) What feature of the formula for this quadratic model indicates that the growth rate eventually increases? The fact that the ---Select--- is ---Select--- 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. The function models the ---Select--- , so the number of broadband users was actually ---Select--- . (f) Pelogrande extrapolated the model to estimate the growth rate at the beginning of 2015 and 2016 (in millions of users). What did he find? (Round your answers to the nearest integer.) n(15) = million users n(16) = million users Comment on the answer. These values are unreasonably large; in fact, their sum exceeds the entire U.S. population. These values seem like a reasonable estimation of broadband users but should be confirmed with more recent data. These values are much smaller than expected, given the widespread use of broadband internet in the U.S.

          Pablo Pelogrande, a new summer intern at OHaganBooks.com in 2015, 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? (Enter your answer using interval notation.)
(b)
According to the model, when was the growth rate at a minimum?
The growth rate was at a minimum at 
t = 
 ,
 midway through 
---Select---
 .
(c)
Does the model predict a zero growth rate at any particular time? If so, when?
Yes, the model has a zero growth rate before 2000.
Yes, the model has a zero growth rate after 2003.    
Yes, the model has a zero growth rate at the minimum.
No, the model does not have a zero growth rate.
(d)
What feature of the formula for this quadratic model indicates that the growth rate eventually increases?
The fact that the 
---Select---
 is 
---Select---
 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.
The function models the 
---Select---
 , so the number of broadband users was actually 
---Select---
 .
(f)
Pelogrande extrapolated the model to estimate the growth rate at the beginning of 2015 and 2016 (in millions of users). What did he find? (Round your answers to the nearest integer.)
n(15) = 
 million users
n(16) = 
 million users
Comment on the answer.
These values are unreasonably large; in fact, their sum exceeds the entire U.S. population.
These values seem like a reasonable estimation of broadband users but should be confirmed with more recent data.    
These values are much smaller than expected, given the widespread use of broadband internet in the U.S.

Added by Adriana G.

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