Chapter 1, Problem 67RE

a.

To determine

To find: the exponential regression equation for the data and superimpose its graph on a scatter plot of the data.

Answer to Problem 67RE

  $y=19092{(1.0025)}^x$ .

Explanation of Solution

Given information: shows the population of New York State for several years. Let $x=0$ represent 2000, $x=1$ represent 2001, and so forth.

Year	Population (thousands)
2003	19,231
2004	19,301
2005	19,336
2006	19,367
2007	19,429
2008	19,490

Calculation:

Let $x=0$ represent 2000, $x=1$ represent 2001, and so forth, then the above table can be written as

Year	Number of Degrees
3	19,231
4	19,301
5	19,336
6	19,367
7	19,429
8	19,490

Using exponential regression calculator on the above data, the exponential regression model is:

  $y=19092{(1.0025)}^x$ .

The graph of the exponential model $y=19092{(1.0025)}^x$ ,using graphing utility is shown below.

  

b.

To determine

To predict: predict the population in 2009, using the regression equation.

Answer to Problem 67RE

  $19,526\text{thousand}\text{people}$ .

Explanation of Solution

Given information: $y=19092{(1.0025)}^x$ .

Calculation:

  $\begin{array}{c}$ y=19092{(1.0025)}^x$\text{For}2009,t=9\\ $ y(9)=19092{(1.0025)}^9$\approx 19,526\text{thousand}\text{people}\text{.}\end{array}$

c.

To determine

To estimate: the annual rate of growth of the population of New York State using the exponential regression equation.

Answer to Problem 67RE

  $0.25\%$ .

Explanation of Solution

Given information: $y=19092{(1.0025)}^x$

Calculation:

The regression equation $y=19092{(1.0025)}^x$ has a base of 1.0025. The base is 1 + annual rate of growth. Letting r be the annual rate of growth then gives:

1+ r = 1.0025 $\to r=0.0025=0.25\%.$