Chapter 3.3, Problem 62E

Solution

(a)

To calculate: regression model for population.

Regression model:

  

Given information:

Year	Population
$\text{1970}$	$\text{717,372}$
$\text{1980}$	$\text{636,297}$
$\text{1990}$	$628,088$
$\text{2000}$	$596,974$
$\text{2010}$	$594,833$

Formula used: definition.

Calculation:

Use a graphing calculator. Enter the t-values on this:

  $\begin{array}{l}L1(1970=10)\\ 1980=20\end{array}$

And population (p) on $L2$. Then feature to find exponential regression for population Milwaukee:

  $p(t)=722230.8094{(0.995625401)}^t$

  

(b)

To calculate: regression model for population.

  

Given information:

Year	Population
$\text{1970}$	$\text{717,372}$
$\text{1980}$	$\text{636,297}$
$\text{1990}$	$628,088$
$\text{2000}$	$596,974$
$\text{2010}$	$594,833$

Formula used: definition.

Calculation:

Scatter plot with the model is shown below. Use zoom stat and adjust window for the graph:

  

(c)

To calculate: regression model for population.

In 2044

Given information:

Year	Population
$\text{1970}$	$\text{717,372}$
$\text{1980}$	$\text{636,297}$
$\text{1990}$	$628,088$
$\text{2000}$	$596,974$
$\text{2010}$	$594,833$

Formula used: definition.

Calculation:

Graph $y=5000000$

together with graph from part (b). Using intersect feature, determine point of intersection of two graphs:

  

(d)

To calculate: computer model realistic why.

No

Given information:

Year	Population
$\text{1970}$	$\text{717,372}$
$\text{1980}$	$\text{636,297}$
$\text{1990}$	$628,088$
$\text{2000}$	$596,974$
$\text{2010}$	$594,833$

Formula used: definition.

Calculation:

The x-coordinate of intersection is $x=84$ so population of Milwaukee will drop to $500,000$ in $1960+84=2044$ .

No, because model will eventually decrease to 0 and will give negative population as t increases.