The US Census Bureau determined that from 1910 to 2010 the US population increas

Question

The US Census Bureau determined that from 1910 to 2010 the US population increased by approximately 1.5% each year. The 13th US Census conducted in 1910 determined that the US population was 92.228 million people. a. What is the 6-year growth factor? Preview b. What was the population of the United States in 1916? million people Preview c. The population in 1938 is how many times as large as the population in 1932? times as large Previevw d. Determine in what year the population of the United States was 111.8 million people. Preview

Explanation / Answer

the exponential function for this scenario can be written as

y = 92.228 (1.015)^x

a) 6 year growth factor is

(1.015)^6 = 1.093 ( rounded to 3 decimal places )

b) population in 1916

plug x = 6

y = 92.228 (1.015)^6

= 100.846

c) population in 1938

92.228 (1.015) ^28

population in 1932

92.228 (1.015) ^22

so population in 1938 is 1.015^6 times that of 1932

d) 111.8 = 92.228 (1.015)^x

111.8/92.228 = (1.015)^x

12.92 or approximately 13

so in the year 1923 population will be 111.8 million

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