### Home > A2C > Chapter Ch3 > Lesson 3.1.6 > Problem 3-78

According to the U.S. Census Bureau, the population of the United States has been growing at an average rate of approximately 2% per year. The census is taken every 10 years, and the population in 1980 was estimated at 226 million people. Homework Help ✎

How many people would the Census Bureau have expected to count in the 1990 census?

How many people should the Census Bureau have expected to count in the 2000 census?

How does your answer compare with the actual 2000 census population data of 281.4 million? What does this mean?

If the rate of population growth in the U.S. had continued at about 2%, in about what year would the population in the United States reach and surpass one billion?

Use the multiplier and the year 1980 as year 0 to write an equation.

226(1.02)^{10} = 275.5 million

See part (a).

How great is the error? Is the population growth faster or slower than expected?

How many million is one billion? Substitute this into the equation you wrote in part (a).

1000 = 226(1.02)^{x}

4.42 = (1.02)^{x}

2055

You will need to guess and check to figure out *x*.