Whooping Cranes

In this project we are going to compare the difference between using a quadratic function and an exponential function to extrapolate population size. The table below gives the maximum number of whooping cranes observed at the Aransas National Wildlife Refuge in Texas from 1938-1996 starting in the winter of each year. For example, the count for 1996 represents the maximum number observed during the winter of 1996-1997.

Numbers of Whooping Cranes at Aransas NWR

Let x = 0 for the year 1938 and using a statistical package or a graphing calculator make a scatterplot in terms of the number of years since 1938 as the independent variable and the number of whooping cranes observed for that year for the dependent variable. With a statistical package or a graphing calculator fit a quadratic equation to this data set. Using this quadratic equation, predict the number of whooping cranes for next year and for the year 1900.

With a statistical package or a graphing calculator fit an equation of the form ln y = . . . . Rewrite this equation using properties of exponents so it is of the form y = . . . . Use this equation to predict the number of whooping cranes for next year and for the year 1900.

Compare your quadratic predictions with your exponential predictions. Which equation do you think gives the better prediction, the quadratic or exponential? Explain.

Related Links:

The Magnificent Whooping Crane