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%.

Question

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%.

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.
Use this formula
y=a*(1-r)^x
Answer:

Answer 1

To model the population of Western Lowland Gorillas after 5, 10, and 20 years, we can use the formula:

y = a * (1 - r)^x

Where:
y = population after x years
a = initial population in 2022 (360,000 gorillas)
r = annual population decline rate (2.7% or 0.027)
x = number of years since 2022

1. Population after 5 years:
x = 5
y = 360,000 * (1 - 0.027)^5
y ≈ 360,000 * (0.973)^5
y ≈ 360,000 * 0.888
y ≈ 319,680
After 5 years, the predicted population of Western Lowland Gorillas is approximately 319,680.

2. Population after 10 years:
x = 10
y = 360,000 * (1 - 0.027)^10
y ≈ 360,000 * (0.973)^10
y ≈ 360,000 * 0.847
y ≈ 305,520
After 10 years, the predicted population of Western Lowland Gorillas is approximately 305,520.

3. Population after 20 years:
x = 20
y = 360,000 * (1 - 0.027)^20
y ≈ 360,000 * (0.973)^20
y ≈ 360,000 * 0.818
y ≈ 294,480
After 20 years, the predicted population of Western Lowland Gorillas is approximately 294,480.

Answer 2

Use the information calculated in step A to create a table showing the Gorilla population after 5, 10 and 20 years.

Answer 3

Here is a table showing the predicted population of Western Lowland Gorillas after 5, 10, and 20 years:

| Years Since 2022 | Population of Gorillas |
|------------------|-----------------------|
| 5 | 319,680 |
| 10 | 305,520 |
| 20 | 294,480 |

Answer 4

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 sentences.

Answer: The table shows exponential decay because [type your answer here]. Scientists can use exponential decay to predict population changes in endangered species by [type your answer here].

Answer 5

The table shows exponential decay because the population of Western Lowland Gorillas is declining at a consistent rate of 2.7% per year. Scientists can use exponential decay to predict population changes in endangered species by using mathematical models to estimate future population sizes based on current data and known population decline rates. Exponential decay allows them to make predictions and assess the impact of conservation efforts on the species' population.