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?

   Hint (a):

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

   Answer (a):

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

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

   Hint (b):

   See part (a).

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

   Hint (c):

   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?