CPM Homework Help : A2C Problem 8-21

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.

Hint (a):

Which functions level off eventually?

Answer (a):

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

Step 1(b):

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

$72000 = a + 60000$

$12000 = a$

$b \approx 0.93$

Step 2(b):

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

$10379 = 12000(b)^2$

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

Answer (b):

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