Superlesson
Project 9-1
Advanced Algebra
Chapter 9, Exponential and Logarithmic Functions
Exponential functions can be used to model the growth and decline of populations of endangered species.
Part B, Exponential Growth and Decay
1. Read about population changes that the bald eagle, America's national bird, has undergone during the past 200 years.
a. Give estimated numbers of bald eagles in the United States in 1800, 1960, and 1995. (Note that the given data are for pairs of eagles.
b. Calculate the average annual rate of decline in the bald eagle population from 1800 to 1960. Calculate the average annual rate of increase from 1960 to 1995.
c. Write and graph equations modeling the population decline (1800-1960) and population increase (1960-1995).
d. If the population decline had not been halted, when would the bald eagle population have fallen below 10 birds (5 pairs)? Without intervention, when would have the species become extinct?
e. If the current rate of increase continues, when will the population exceed the 1800 population?
Part C, Modeling Exponential Growth and Decay
2. Like the bald eagle before it rebounded, the whooping crane is a gravely endangered species.
a. Collect and graph data on whooping crane numbers, 1940-1996.
b. Use exponential regression to find an exponential model y = abx of the data. Round a and b to the nearest thousandth.
c. Use your model to estimate the year in which the whooping crane population reached 100 birds.
Part E, Making Connections
3. The California condor is another gravely endangered bird. Read the life history of the California condor.
a. Because of the success of captive breeding programs, the number of condors alive in 1987 soon doubled. How many years did it take the number of condors to double?
b. Use the Rule of 70 to approximate the rate of increase in condor numbers during the doubling period. Assume continuous exponential growth.
c. Write and graph an equation that models continuous exponential growth during the population doubling period that began in 1987.
d. If your model is correct, how many condors will be alive in the year 2000?
e. Is an exponential model a good one for modeling condor population growth? Explain.