Every year, endangered species experience population decline and are pushed
closer to extinction. This decline in population is mostly caused by human
destruction of these species’ natural habitat. The Western Lowland Gorilla is an
example of an endangered species. In 2022, there are 360,000 Western
Lowland Gorillas remaining, with an annual population decline of 2.7%.
a. Use what you’ve learned in this unit to model the population of Western
Lowland Gorillas after 5, 10 and 20 years. Let y equal the population of the
gorillas and x represent the number of years since 2022. Show your work.
b. Use the information calculated in step A to create a table showing the Gorilla
population after 5, 10 and 20 years.
c. Explain why the table shows exponential decay. Summarize how scientists
can use exponential decay to predict population changes in endangered
species. Summarize your answer in 1-2 paragraphs.
a. To model the population of Western Lowland Gorillas after 5, 10, and 20 years, we can use the exponential decay formula: y = A(1 - r)^x, where A is the initial population (360,000 gorillas in 2022), r is the annual decline rate (2.7% or 0.027), and x is the number of years since 2022.
For 5 years: y = 360,000(1 - 0.027)^5 ≈ 314,714 gorillas remaining
For 10 years: y = 360,000(1 - 0.027)^10 ≈ 274,679 gorillas remaining
For 20 years: y = 360,000(1 - 0.027)^20 ≈ 190,284 gorillas remaining
b. The table showing the Gorilla population after 5, 10, and 20 years would be:
| Years | Population |
|-------|------------|
| 5 | 314,714 |
| 10 | 274,679 |
| 20 | 190,284 |
c. The table shows exponential decay because the population of Western Lowland Gorillas is declining at a constant rate of 2.7% per year. The formula y = A(1 - r)^x, where r is less than 1, represents exponential decay. As the years go by, the population decreases exponentially.
Scientists can use exponential decay to predict population changes in endangered species by studying the decline rate and using mathematical models to estimate future populations. By analyzing the factors contributing to the decline, such as habitat destruction, climate change, or poaching, scientists can use exponential decay models to make predictions and determine conservation strategies for the species. This helps in understanding the urgency of conservation efforts and planning measures to save the endangered species from extinction.