Question

the accompanying table of a particular countrys resident population and land area for selected years from 1800 through 2019. use the information to complete parts (a) and (b) below.
a. find the population density of the country, to the nearest tenth, in 1900 and in 2019
b. find the percent increase in population density, to the nearest tenth of a percent, from 1900 to 2019
a. the population density, to the nearest tenth, in 1900 was 23.8 people per square mile (round to the nearest tenth as needed.)
the population density, to the nearest tenth, in 2019 was \\(\square\\) (round to the nearest tenth as needed.)
figure
1800 5,308,483 864,746
1900 71,026,752 2,966,711
1940 131,669,275 2,971,128
1980 226,545,805 3,539,289
2019 284,364,791 3,685,096

Explanation:

Part (a) - 2019 Population Density

Step 1: Recall Population Density Formula

Population density is calculated as $\text{Population Density} = \frac{\text{Population}}{\text{Land Area}}$.

Step 2: Identify 2019 Population and Land Area

From the table, the 2019 population is $284,364,791$ and the land area is $3,685,096$ square miles.

Step 3: Calculate Population Density

Divide the population by the land area: $\frac{284364791}{3685096}$.

Using a calculator, $\frac{284364791}{3685096} \approx 77.2$ (rounded to the nearest tenth).

Step 1: Recall Percent Increase Formula

The percent increase formula is $\text{Percent Increase} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\%$.

Step 2: Identify Old and New Values

The old value (1900 population density) is $23.8$ people per square mile. The new value (2019 population density) is $77.2$ people per square mile.

Step 3: Calculate the Difference

Find the difference: $77.2 - 23.8 = 53.4$.

Step 4: Calculate Percent Increase

Divide the difference by the old value and multiply by 100: $\frac{53.4}{23.8} \times 100\%$.

Using a calculator, $\frac{53.4}{23.8} \times 100\% \approx 224.4\%$ (rounded to the nearest tenth of a percent).

Answer:

77.2 people per square mile

Part (b) - Percent Increase in Population Density