Chapter 1.3, Problem 20E

(a)

To determine

To find: The ratios of the population in one year by the population in previous year.

Answer to Problem 20E

The ratios of the population in one year by the population in previous year are $1.0122$ , $1.0126$ , $1.0125$ , $1.0108$ and $1.0094$ .

Explanation of Solution

Given information:

Table below gives the population of Virginia for several years:

Population of Virginia
Year	Population(Thousands)
$2002$	$7282$
$2003$	$7371$
$2004$	$7464$
$2005$	$7558$
$2006$	$7640$
$2007$	$7712$

Calculation:

The ratio of the population in $2003$ by the population in $2002$ is

  $\frac{7371}{7282}=1.0122$

The ratio of the population in $2004$ by the population in $2003$ is

  $\frac{7464}{7371}=1.0126$

The ratio of the population in $2005$ by the population in $2004$ is

  $\frac{7558}{7464}=1.0125$

The ratio of the population in $2006$ by the population in $2005$ is

  $\frac{7640}{7558}=1.0108$

The ratio of the population in $2007$ by the population in $2006$ is

  $\frac{7712}{7640}=1.0094$

Therefore, the ratios of the population in one year by the population in previous year are $1.0122$ , $1.0126$ , $1.0125$ , $1.0108$ and $1.0094$ .

(b)

To determine

To find:The exponential model for the population of Virginia.

Answer to Problem 20E

The exponential model for the population of Virginiais $7282{\left(1.01\right)}^n$ .

Explanation of Solution

Given information:

Table below gives the population of Virginiafor several years:

Population of Virginia
Year	Population(Thousands)
$2002$	$7282$
$2003$	$7371$
$2004$	$7464$
$2005$	$7558$
$2006$	$7640$
$2007$	$7712$

Calculation:

The population of Virginiabecomes $1.01$ times every year.

Take $n=0$ for the year $2002$ and the population in the initial year is $7282$ thousands.

The exponential function for the population of Virginiais:

  $y=7282{\left(1.01\right)}^n$

Therefore, the exponential model for the population of Virginiais $7282{\left(1.01\right)}^n$ .

(c)

To determine

To find:The population of Virginiain $2012$ with the help of exponential model.

Answer to Problem 20E

The population of Virginiain $2012$ is $8043.85$ thousands.

Explanation of Solution

Given information:

Table below gives the population of Nevada for several years:

Population of Nevada
Year	Population(Thousands)
$2002$	$7282$
$2003$	$7371$
$2004$	$7464$
$2005$	$7558$
$2006$	$7640$
$2007$	$7712$

Calculation:

As calculated in part (b), the exponential model for the population of Virginiais:

  $y=7282{\left(1.01\right)}^n$

The initial value for $n$ is zero in the year $2002$ . So, the value $n=10$ corresponds to the year $2012$ .

Substitute $10$ for $n$ in the exponential model.

  $y=7282{\left(1.01\right)}^{10}$

Use the calculator for the value of $7282{\left(1.01\right)}^{10}$ . Press “ON” button and enter the keystrokes as given below:

  $\boxed{7282}\boxed{\times }\boxed{(}\boxed{1.01}\boxed{)}\boxed{^}\boxed{10}$

The value of $7282{\left(1.01\right)}^{10}$ is $8043.85$ thousands.

Therefore, the population of Virginiain $2012$ is $8043.85$ thousands.