Question

the population density is about 4614 people per square mile.
visit www.bigideasmathvideos.com to watch the flipped video instruction for the \try this\ problem(s) below.
try this video for extra example 1 – finding a population density

1. the state of colorado has a population of about 5 million people. find the population density in people per square mile. hint: find the area of the rectangular region.

image of colorado map with dimensions 375 mi (width) and 275 mi (height)

Explanation:

Step1: Calculate the area of Colorado (rectangle)

The area \( A \) of a rectangle is given by \( A = \text{length} \times \text{width} \). Here, length \( l = 375 \) mi and width \( w = 275 \) mi. So, \( A = 375 \times 275 \).

$$ 375 \times 275 = (300 + 75) \times (200 + 75) = 300\times200 + 300\times75 + 75\times200 + 75\times75 = 60000 + 22500 + 15000 + 5625 = 103125 \text{ square miles} $$

Step2: Calculate population density

Population density \( d \) is given by \( d = \frac{\text{Population}}{\text{Area}} \). The population is \( 5000000 \) people and area is \( 103125 \) square miles. So, \( d = \frac{5000000}{103125} \).

$$ \frac{5000000}{103125} \approx 48.5 $$

Answer:

The population density of Colorado is approximately \( 48.5 \) people per square mile.