Several years ago, a large city undertook a major effort to encourage carpooling in order to reduce traffic congestion. The accompanying table shows the number of carpoolers, in thousands, from 2007 to 2012 . Use regression to obtain a function f(x)=a+b ln x that models the data, where x=1 corresponds to 2007, x=2 to 2008, and so on. Round the constants a and b to the nearest hundredth.
$\begin{array} { l | c | c | c | c | c | c }
\text { Year } & 2007 & 2008 & 2009 & 2010 & 2011 & 2012 \
\hline \text { Carpoolers } & 3.9 & 8.1 & 10.3 & 11.8 & 12.6 & 13.2
\end{array}$
A) f(x)=4.22+5.25ln x
B) f(x)=4.33+5.17ln x
C) f(x)=4.29+5.14ln x
D) f(x)=4.40+5.32ln x

Question

Several years ago, a large city undertook a major effort to encourage carpooling in order to reduce traffic congestion. The accompanying table shows the number of carpoolers, in thousands, from 2007 to  2012 .  Use regression to obtain a function  f(x)=a+b ln x  that models the data, where  x=1  corresponds to  2007, x=2  to 2008, and so on. Round the constants a and b to the nearest hundredth.
$\begin{array} { l | c | c | c | c | c | c } 
\text { Year } & 2007 & 2008 & 2009 & 2010 & 2011 & 2012 \
\hline \text { Carpoolers } & 3.9 & 8.1 & 10.3 & 11.8 & 12.6 & 13.2
\end{array}$
A)  f(x)=4.22+5.25ln x 
B)  f(x)=4.33+5.17ln x 
C)  f(x)=4.29+5.14ln x 
D)  f(x)=4.40+5.32ln x

Quizplus · Accepted Answer

The given data can be modeled by the function f(x) = a + b ln x, where x = 1 corresponds to 2007, x = 2 to 2008, and so on. Using regression, we can find the values of a and b that best fit the data. The correct answer is A: f(x) = 4.22 + 5.25 ln x.

Several Years Ago, a Large City Undertook a Major Effort