### Home > A2C > Chapter 8 > Lesson 8.1.2 > Problem8-21

8-21.
1. 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. Homework Help ✎

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

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

Which functions level off eventually?

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

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

$72000 = a + 60000$

$12000 = a$

$b \approx 0.93$

$70379 = a(b)^0 + 60000$

$10379 = 12000(b)^2$

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

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