a. To model the population of Western Lowland Gorillas after 5, 10, and 20 years, we can use the formula for exponential decay: y = a(1 - r)^x, where y is the population after x years, a is the initial population (360,000 gorillas), and r is the annual population decline rate (2.7% or 0.027).
After 5 years (x = 5):
y = 360,000(1 - 0.027)^5
y ≈ 360,000(0.973)^5
y ≈ 360,000(0.8864)
y ≈ 319,904 gorillas
After 10 years (x = 10):
y = 360,000(1 - 0.027)^10
y ≈ 360,000(0.973)^10
y ≈ 360,000(0.8490)
y ≈ 305,639 gorillas
After 20 years (x = 20):
y = 360,000(1 - 0.027)^20
y ≈ 360,000(0.973)^20
y ≈ 360,000(0.7350)
y ≈ 264,600 gorillas
b. Table showing the Gorilla population after 5, 10, and 20 years:
| Years | Population |
| --------- | ---------- |
| 5 | 319,904 |
| 10 | 305,639 |
| 20 | 264,600 |
c. The table shows exponential decay because the population decreases over time at a constant percentage rate (2.7% per year). Exponential decay occurs when each value of a variable is multiplied by some constant factor (1 - r) to get the next value, resulting in a rapidly declining population.
Scientists can use exponential decay to predict population changes in endangered species because it provides a mathematical model that estimates how the population will decrease over time. By knowing the initial population and the annual decline rate, scientists can make projections for future populations. This information is crucial for conservation efforts and can help determine the urgency and effectiveness of different strategies aimed at preserving endangered species.
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.
1 answer