Question

the accompanying bar graph shows the resident population and the land area of a particular county for selected years from 1900 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.

click here to view a bar graph showing resident population and the land area of a particular county for selected years from 1900 through 2019.

a. the population density, to the nearest tenth, in 1900 was 20.8 people per square mile
(round to the nearest tenth as needed.)

the population density, to the nearest tenth, in 2019 was 77.2 people per square mile
(round to the nearest tenth as needed.)

b. the percent increase in population density from 1900 to 2019 was %
(round to the nearest tenth as needed.)

Explanation:

Part b: Percent Increase in Population Density

Step 1: Recall the percent increase formula

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

Step 2: Identify the old and new values

• Old value (1900 population density): $20.8$ people per square mile.
• New value (2019 population density): $77.2$ people per square mile.

Step 3: Substitute into the formula

First, calculate the difference: $77.2 - 20.8 = 56.4$.

Then, divide by the old value: $\frac{56.4}{20.8}$.

Finally, multiply by 100%: $\frac{56.4}{20.8} \times 100\%$.

Step 4: Perform the calculation

$\frac{56.4}{20.8} \approx 2.7115$

$2.7115 \times 100\% = 271.15\% \approx 271.2\%$ (rounded to the nearest tenth).

Answer:

The percent increase in population density from 1900 to 2019 was $\boxed{271.2}\%$.