Question

Suppose the geographic areas of California and the U.S. are 1.637 x 10⁹ and 3.794 x 10⁶ sq. m, respectively. California's population (as of 2012) is approximately 3.804 x 10⁷ people. If population were proportional to area, what would be the U.S. population?

A. ( 3.794 × 10⁶/1.637 × 10⁹ × 3.804 × 10⁷ )
B. ( 3.794 × 10⁹/1.637 × 10⁶ × 3.804 × 10⁷ )
C. ( 3.794 × 10⁶/3.804 × 10⁷ × 1.637 × 10⁹ )
D. ( 1.637 × 10⁹/3.804 × 10⁷ × 3.794 × 10⁶ )

Answer 1

The U.S. population, if proportional to the area compared to California's population, is calculated with the formula (U.S. area / California's area) × California's population, which matches option A.

Step-by-step explanation:

If population were proportional to area, we should expect the ratio of the populations of two regions to be the same as the ratio of their areas. To find the U.S. population under the assumption that it is proportional to California's population with respect to their geographic areas, we use the formula:

U.S. population = (California's population / California's area) × U.S. area.

Substituting the given values, we obtain:

U.S. population = (3.804 × 10⁷ people / 1.637 × 10⁹ sq. m) × 3.794 × 10⁶ sq. m

This formula aims to find the proportion of the U.S. population to the area relative to California's known population and area figures. The correct representation of this statement is found in option A:

( 3.794 × 10⁶ / 1.637 × 10⁹ × 3.804 × 10⁷ )