Chapter 11.4, Problem 26E

Solution

a.

To find: The average velocity $\frac{\Delta y}{\Delta x}$ on each subinterval of length $0.5$ . Also, create a table showing midpoints and average velocities.

The table 1 shows the midpoints of subintervals of length $0.5$ and average velocities.

Given information: The table below shows the population growth of Clark County:

Year	Population
$1910$	$3321$
$1920$	$4859$
$1930$	$8532$
$1940$	$16414$
$1950$	$48289$
$1960$	$127016$
$1970$	$273288$
$1980$	$463087$
$1990$	$741368$
$2000$	$1375741$
$2010$	$1951269$
$2016$	$2155664$

Calculation:

Make a table that shows the midpoints and average velocities at on each subinterval of length $0.5$ .

Midpoint	$\frac{\Delta y}{\Delta x}$
$15$	$153.8$
$25$	$367.3$
$35$	$788.2$
$45$	$3187.5$
$55$	$7872.7$
$65$	$14627.2$
$75$	$18979.9$
$85$	$27828.1$
$95$	$63237.3$
$105$	$57552.8$
$113$	$34065.8$

Table (1)

Thus, the above table shows the midpoints of subintervals of length $0.5$ and average velocities.

b.

To calculate: The scatter plot of the of the data and the time of occurrence of the average rate of change.

The scatter plot of the data is shown in figure (1) and the greatest average rate of change occurred in year between $1990$ and $2000$ after that it declined slowly in growth.

Given information: The table below shows the population growth of Clark County:

Year	Population
$1910$	$3321$
$1920$	$4859$
$1930$	$8532$
$1940$	$16414$
$1950$	$48289$
$1960$	$127016$
$1970$	$273288$
$1980$	$463087$
$1990$	$741368$
$2000$	$1375741$
$2010$	$1951269$
$2016$	$2155664$

Graph:

To draw scatter plot of the data in table 1 of part (a), under $\text{L}1$ enters the midpoints and under $\text{L}2$ enter the average rate of change. Plot the graph in the viewing window $\left[0,120\right]$ by $\left[-10000,70000\right]$ as shown below.

  

Figure (1)

Thus, the scatter plot of the data is shown in figure (1) and the greatest average rate of change occurred in year between $1990$ and $2000$ after that it declined slowly in growth.