n exponential function is a good model for population growth when the growth rate stays relatively constant. This type of function can also be used to model the number of people with a contagious disease in the early stages of an epidemic. However, there are usually limits on growth. Populations are eventually limited by finite space and resources. Diseases cannot infect more than 100% of the population, and they may also be limited by social policies, medical treatments, and growing immunity in the population.

8. It's your turn to find some real-world data to model with an exponential function or a logistic function.

• Identify the data you want to analyze. Your data should includeat least 8 ordered pairs.
• Plot the points on a handheld or online graphing calculator.
• Decide which model to use: exponential or logistic. Justify your choice in writing.
• Using that model, find a function that models your data well. The work you turn in should
• tell where you found your data,
• list the data in a table,
• justify your choice of model, and
• give the function that is a good fit for your data.

Data search tips: If you're interested in logistic functions, look for

• population data (human or animal) for a small island or other area with limited space; or
• data on the number of people in a country/state/city who caught an infectious disease. Choose a disease for which the number of infected people is no longer growing quickly.

If you're interested in exponential functions, look for

• data for a population's first years of growth in a large area, such as right after a species was introduced or a city was founded; or
• data on the number of people who caught an infectious disease, starting when the disease was first identified and going through the time it was spreading most rapidly.

(16 points: 4 points for finding suitable data, 4 points for choosing the appropriate model, and up to 8 points for the function modeling the data, depending on how well it fits the data)