Questions: Let p(t) represent the population of the Las Vegas metropolitan area t years after 1970, as shown in the table and figure. Answer parts (a) through (c). Year 1970 1980 1990 t 0 10 20 p(t) 305,000 528,000 853,000 Year 2000 2010 2020 t 30 40 50 p(t) 1,563,000 1,951,000 2,223,000 Source: U.S. Bureau of Census a. Compute the average rate of growth of the city population from 1980 to 1990. The average rate of growth is people/year. (Simplify your answer. Type an integer or a decimal.)

Let p(t) represent the population of the Las Vegas metropolitan area t years after 1970, as shown in the table and figure. Answer parts (a) through (c).

Year 1970 1980 1990
t 0 10 20
p(t) 305,000 528,000 853,000
Year 2000 2010 2020
t 30 40 50
p(t) 1,563,000 1,951,000 2,223,000

Source: U.S. Bureau of Census

a. Compute the average rate of growth of the city population from 1980 to 1990.

The average rate of growth is people/year. (Simplify your answer. Type an integer or a decimal.)

Transcript text: Let $p(t)$ represent the population of the Las Vegas metropolitan area $t$ years after 1970, as shown in the table and figure. Answer parts (a) through (c). \begin{tabular}{lccc} \hline Year & 1970 & 1980 & 1990 \\ \hline t & 0 & 10 & 20 \\ $\mathrm{p}(\mathrm{t})$ & 305,000 & 528,000 & 853,000 \\ \hline Year & 2000 & 2010 & 2020 \\ \hline t & 30 & 40 & 50 \\ $\mathrm{p}(\mathrm{t})$ & $1,563,000$ & $1,951,000$ & $2,223,000$ \\ \hline \end{tabular} Source: U.S. Bureau of Census a. Compute the average rate of growth of the city population from 1980 to 1990. The average rate of growth is $\square$ people/year. (Simplify your answer. Type an integer or a decimal.)

Solution

Solution Steps

Step 1: Identify the given data

The problem provides population data for the Las Vegas metropolitan area at different years after 1970. The years and corresponding populations are:

1980 (t = 10): 528,000
1990 (t = 20): 853,000

Step 2: Calculate the change in population

To find the average rate of growth, we first need to determine the change in population between 1980 and 1990. \[ \Delta p = p(1990) - p(1980) = 853,000 - 528,000 = 325,000 \]

Step 3: Calculate the change in time

Next, we calculate the change in time between 1980 and 1990. \[ \Delta t = 1990 - 1980 = 10 \text{ years} \]

Step 4: Compute the average rate of growth

The average rate of growth is the change in population divided by the change in time. \[ \text{Average rate of growth} = \frac{\Delta p}{\Delta t} = \frac{325,000}{10} = 32,500 \text{ people/year} \]