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 $60,000$ .

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.
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):

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

$10379 = 12000(b)^2$

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

Answer (b)

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