The function is , where is the number of decades after .

Observe the graph :

. 

As the number of decades since increases with out bound, the population increases with out bound.

Support numerically:

Construct a table that shows the values to investigate the function values as of  increases. 

Observe the table:

As tends to , approaches to .

.

As the number of decades since increases with out bound, the population increases with out bound.

The population trend does not seem realistic because there is no way to guarantee that the U.S. population will increase with out bound in future.

As the number of decades since   increases with out bound, the population increases with out bound.

The population trend does not seem realistic.