### Home > CCA2 > Chapter 7 > Lesson 7.1.2 > Problem7-20

7-20.

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?

Which functions level off eventually?

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.

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

$72000 = a + 60000$

$12000 = a$

$b \approx 0.93$

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

$10379 = 12000(b)^2$

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

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