### Home > AC > Chapter 14 > Lesson 14.3.1.6 > Problem3-78

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.

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

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

$226\left(1.02\right)^{10} = 275.5 \text{ million}$

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

See part (a).

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

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

4. 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?

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.