In 1998, Terre Haute, Indiana had a population of $72,000$ people. In 2000, the population had dropped to $70,379$. City officials expect the population to level off eventually at $60,000$.

1. What kind of function would best model the population over time?

   Hint (a):

   Which functions level off eventually?

   Answer (a):

   An exponential function with an asymptote at y = 60,000 would be the best model.

2. Write an equation that would model the changing population over time.

   Step 1(b):

   $72000 = a(b)^0 + 60000$

   $72000 = a + 60000$

   $12000 = a$

   $b \approx 0.93$
   

   Step 2(b):

   $70379=a(b)^2+60000$

   $10379 = 12000(b)^2$

   $\frac{10379}{12000} = b^2$

   Answer (b):

   $y = 12000(0.93)^t + 60000$