(a) Answer The ratios of the population in one year by the population in previous year are 1.0322 , 1.0411 , 1.0339 , 1.0344 and 1.0292 . Explanation Given information: Table below gives the population of Nevada for several years: Population of Nevada Year Population(Thousands) 2002 2168 2003 2238 2004 2330 2005 2409 2006 2492 2007 2565 Calculation: The ratio of the population in 2003 by the population in 2002 is: 2238 2168 = 1.0322 The ratio of the population in 2004 by the population in 2003 is: 2330 2238 = 1.0411 The ratio of the population in 2005 by the population in 2004 is: 2409 2330 = 1.0339 The ratio of the population in 2006 by the population in 2005 is: 2492 2409 = 1.0344 The ratio of the population in 2007 by the population in 2006 is: 2565 2492 = 1.0292 Therefore, the ratios of the population in one year by the population in previous year are 1.0322 , 1.0411 , 1.0339 , 1.0344 and 1.0292 . (b) To determine To find: The exponential model for the population of Nevada. Answer The exponential model for the population of Nevada is 2168 ( 1.03 ) n . Explanation Given information: Table below gives the population of Nevada for several years: Population of Nevada Year Population(Thousands) 2002 2168 2003 2238 2004 2330 2005 2409 2006 2492 2007 2565 Calculation: From part (a), the population of Nevada becomes 1.03 times every year. Take n = 0 for the year 2002 and the population in the initial year is 2168 thousands. The exponential function for the population of Nevada is: y = 2168 ( 1.034 ) n Therefore, the exponential model for the population of Nevada is 2168 ( 1.034 ) n . (c) To determine To find: The population of Nevada in 2015 with the help of exponential model. Answer The population of Nevada in 2015 will be 3348 thousands. Explanation Given information: Table below gives the population of Nevada for several years: Population of Nevada Year Population(Thousands) 2002 2168 2003 2238 2004 2330 2005 2409 2006 2492 2007 2565 Calculation: As calculated in part(b), the exponential model for the population of Nevada is: y = 2168 ( 1.034 ) n The initial value for n is zero in the year 2002 . So, the value n = 13 corresponds to the year 2015 . Substitute 13 for n in the exponential model. y = 2168 ( 1.034 ) 13 Use the calculator for the value of 2168 ( 1.034 ) 13 . Press “ON” button and enter the keystrokes as given below: 2168 × ( 1.034 ) ^ 13 The value of 2168 ( 1.03 ) 13 is 3348.31 thousands. Therefore, the population of Nevada in 2015 will be 3348 thousands.

Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Question

Chapter 1.3, Problem 19E

(a)

To determine

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

(a)

Expert Solution

Answer to Problem 19E

The ratios of the population in one year by the population in previous year are $1.0322$ , $1.0411$ , $1.0339$ , $1.0344$ and $1.0292$ .

Explanation of Solution

Given information:

Table below gives the population of Nevada for several years:

Population of Nevada
Year	Population(Thousands)
$2002$	$2168$
$2003$	$2238$
$2004$	$2330$
$2005$	$2409$
$2006$	$2492$
$2007$	$2565$

Calculation:

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

$22382168=1.0322$

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

$23302238=1.0411$

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

$24092330=1.0339$

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

$24922409=1.0344$

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

$25652492=1.0292$

Therefore, the ratios of the population in one year by the population in previous year are $1.0322$ , $1.0411$ , $1.0339$ , $1.0344$ and $1.0292$ .

(b)

To determine

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

(b)

Expert Solution

Answer to Problem 19E

The exponential model for the population of Nevada is $2168(1.03)n$ .

Explanation of Solution

Given information:

Table below gives the population of Nevada for several years:

Population of Nevada
Year	Population(Thousands)
$2002$	$2168$
$2003$	$2238$
$2004$	$2330$
$2005$	$2409$
$2006$	$2492$
$2007$	$2565$

Calculation:

From part (a), the population of Nevada becomes $1.03$ times every year.

Take $n=0$ for the year $2002$ and the population in the initial year is $2168$ thousands.

The exponential function for the population of Nevada is:

$y=2168(1.034)n$

Therefore, the exponential model for the population of Nevada is $2168(1.034)n$ .

(c)

To determine

To find:The population of Nevada in $2015$ with the help of exponential model.

(c)

Expert Solution

Answer to Problem 19E

The population of Nevada in $2015$ will be $3348$ thousands.

Explanation of Solution

Given information:

Table below gives the population of Nevada for several years:

Population of Nevada
Year	Population(Thousands)
$2002$	$2168$
$2003$	$2238$
$2004$	$2330$
$2005$	$2409$
$2006$	$2492$
$2007$	$2565$

Calculation:

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

$y=2168(1.034)n$

The initial value for $n$ is zero in the year $2002$ . So, the value $n=13$ corresponds to the year $2015$ .

Substitute $13$ for $n$ in the exponential model.

$y=2168(1.034)13$

Use the calculator for the value of $2168(1.034)13$ . Press “ON” button and enter the keystrokes as given below:

$2168×(1.034)^13$

The value of $2168(1.03)13$ is $3348.31$ thousands.

Therefore, the population of Nevada in $2015$ will be $3348$ thousands.

Chapter 1.3, Problem 18E

Chapter 1.3, Problem 20E

Chapter 1 Solutions

Calculus: Graphical, Numerical, Algebraic

Ch. 1.1 - Prob. 1QR Ch. 1.1 - Prob. 2QR Ch. 1.1 - Prob. 3QR Ch. 1.1 - Prob. 4QR Ch. 1.1 - Prob. 5QR Ch. 1.1 - Prob. 6QR Ch. 1.1 - Prob. 7QR Ch. 1.1 - Prob. 8QR Ch. 1.1 - Prob. 9QR Ch. 1.1 - Prob. 10QR

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