Use the method of Example 1 to find a logistic function that describes the following populations. Graph the population function.

The population increases from 200 to 600 in the first year and eventually levels off at 2000.

Data from in Example 1

EXAMPLE 1 Designing a logistic model Wildlife biologists observe a prairie dog community for several years. When observations begin, there are 8 prairie dogs; after one year the population reaches 20 prairie dogs. After 10 years, the population has leveled out at approximately 200 prairie dogs. Assuming that a logistic growth model applies to this community, find a function that models the population.