Question

the population of a city from 2005 to 2012 is approximated in the following table. complete parts a through g below.
year 2005 2006 2007 2008 2009 2010 2011 2012
population (in thousands) 112.6 116.7 120.9 125.2 129.7 134.4 139.2 144.2
e. what is the n - intercept? what is the practical meaning of the intercept in this situation?
the n - intercept is (0,112.6).
(type an ordered pair, using integers or decimals.)
what is the practical meaning of the intercept in this situation? select the correct choice below and fill in the answer box to complete your choice.
(type an integer or a decimal.)
○ a. the population of the city in the year 0 was.
● b. the population of the city in the year 2005 was 112,600.
f. use the equation to estimate the population of the city in the year 2034. is this a good estimate? explain.
n = thousand
(type an integer or decimal rounded to one decimal place as needed.)

Explanation:

Step1: Find the slope

Let \(x\) be the number of years since 2005. So for 2005, \(x = 0\); for 2006, \(x=1\); and so on.
We have two points \((x_1,y_1)=(0,112.6)\) and \((x_2,y_2)=(7,144.2)\) (since \(2012 - 2005=7\)).
The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{144.2-112.6}{7}=\frac{31.6}{7}\approx4.514\)

Step2: Write the linear equation

Using the point - slope form \(y - y_1=m(x - x_1)\), with \(x_1 = 0\) and \(y_1=112.6\) and \(m\approx4.514\), the equation is \(N=4.514x + 112.6\)

Step3: Calculate \(x\) for 2034

Since \(2034-2005 = 29\), so \(x = 29\)
Substitute \(x = 29\) into the equation \(N=4.514\times29+112.6\)
\(N=4.514\times29+112.6=130.906+112.6=243.506\approx243.5\)

Step4: Analyze if it is a good estimate

This is not a good estimate. Linear models are best for short - term predictions. Over a long period (29 years in this case), factors like birth rates, death rates, migration patterns, and economic conditions (which can change significantly over time) are not accounted for in a simple linear model.

Answer:

\(N = 243.5\) thousand; No, it is not a good estimate. Linear models are for short - term predictions, and long - term population changes are affected by many complex factors not in the simple linear model.