Graphs

Modeling with Modeling with Logistic Functions A logistic growth model is a function of the form.

Where a, b, and c are positive constants. Logistic functions are used to model populations where the growth is constrained by available resources

Introduction:

In a previous Focus on Modeling project, we learned that the shape of a scatter plot helps us to choose the type of curve to use in modeling data. The first plot in Figure below strongly suggests that a line be fitted through it, and the second one points to a cubic polynomial. For the third plot it is tempting to fit a second-degree polynomial. But what if an exponential curve fits better? How do we decide this? In this project we learn how to fit exponential and power curves to data and how to decide which type of curve fits the data better. We also learn that for scatter plots like those in the last two plots below, the data can be modeled by logarithmic or logistic functions Much of the fish that is sold in supermarkets today is raised on commercial fish farms, not caught in the wild. A pond on one such farm is initially stocked with 1000 catfish, and the fish population is then sampled at 15-week intervals to estimate its size. The population data are given in Table above.

1- Try find an appropriate model for the data.

2- Make a scatter plot of the data and graph the model that you found in part (1) on the scatter plot.

3- Discuss how does the model predict that the fish population will change with time.