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.

Question

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

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

Answer 1

some kind of exponential would do it. So, with t as time since 1998,

f(0) = 72000
f(2) = 70379
f(∞) = 60000

f(t) = 60000 + 12000 e^-kt

now we need k so that f(2) = 70379

60000 + 12000 e^-2k = 10379
k = 0.073

So,

f(t) = 60000 + 12000 e^(-.073t)