The U.S. Census Bureau takes a census every $10$ years. The population in $2000$ was estimated at $281.4$ million people. A model created at the time predicted that the population grew at about $2\%$ per year.

1. How many people would the Census Bureau have expected to count in the $2005$ census?

   Hint (a):

   Write an exponential equation to help you solve this problem.

   Answer (a):

   $y = 281.4\left(1.02\right)^{5}$
   $310.7$ million people

2. If the Census Bureau had conducted a count in $2010$, how many people would it have expected to count?

   Hint (b):

   Refer to part (a), but change it to fit this situation.

3. The actual $2010$ census put the population at $309$ million people. What is the residual? What does it mean?

   Hint (c):

   Is this less than or greater than the expected amount?
   What does that tell you about the population growth?

   Answer(c):

   The residual is $-34$ million. Population growth has slowed.