Chapter 4, Problem 1P

a.

To determine

Make a scatter plot of the data.

Answer to Problem 1P

  

Explanation of Solution

Given information:

The U.S. Constitution requires a census every $10$ year. The census data for $1790$ − $2000$ are given in the table.

  

Calculation:

Sketch the scatter plot data by using graphing calculator,

Press STAT and 1.

  

Enter the given data from the table,

  

Go to $\boxed{2nd}\boxed{y=}$ and then press ENTER.

  

Set the WINDOW.

  

Now click on the GRAPH option.

  

Hence, the solution is,GRAPH.

b.

To determine

Use a calculator to find an exponential model for the data.

Answer to Problem 1P

  

Explanation of Solution

Given information:

The U.S. Constitution requires a census every $10$ year. The census data for $1790$ − $2000$ are given in the table.

  

Calculation:

  $\boxed{STAT}\boxed{CALC}$ and enter Zero for exponential regression.

  

Press Enter the exponential model for the data.

  

The exponential model for the data.

  $y=ab\text{'}$

Where $a=1.181\times {10}^{-15}$ and $b=1.020,$

  $y$ is the population in millions in the $t$ years.

Hence, the solution is,GRAPH.

c.

To determine

Use your model to predict the population at the $2010$ census.

Answer to Problem 1P

  $\boxed{516.11million}$

Explanation of Solution

Given information:

The U.S. Constitution requires a census every $10$ year. The census data for $1790$ − $2000$ are given in the table.

  

Calculation:

To calculate the population in $2010$ substitute $2010$ in the exponential model.

  $\begin{array}{l}y\left(2010\right)=\left(1.181\times {10}^{-15}\right){\left(1.020\right)}^{2010}\\ =516.11\end{array}$

Therefore, the population in $2010$ is $\boxed{516.11million}$

Hence, the solution is, $\boxed{516.11million}$

d.

To determine

Use your model to estimate the population in $1965$ .

Answer to Problem 1P

  $\boxed{207.87million}$

Explanation of Solution

Given information:

The U.S. Constitution requires a census every $10$ year. The census data for $1790$ − $2000$ are given in the table.

  

Calculation:

To calculate the population in $1965$ substitute $1965$ in the exponential model.

  $\begin{array}{l}y\left(1965\right)=\left(1.181\times {10}^{-15}\right){\left(1.020\right)}^{1965}\\ =207.87\end{array}$

Therefore, the population in $1965$ is $\boxed{207.87million}$

Hence, the solution is, $\boxed{207.87million}$

e.

To determine

Compare your answers from parts $\left(c\right)$ and $\left(d\right)$ to the values in the table. Do you think an exponential model is appropriate for these data?

Answer to Problem 1P

Exponential model is not appropriate for the data.

Explanation of Solution

Given information:

The U.S. Constitution requires a census every $10$ year. The census data for $1790$ − $2000$ are given in the table.

  

Calculation:

The value that is calcululated is higher then the actual data in the year $1970$ . So the exponential model is not appropriate for the data.

Hence, the exponential model is not appropriate for the data.