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:
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 of gorillas after x years
a = initial population (360,000 gorillas)
r = annual population decline rate (2.7% or 0.027)
x = number of years since 2022
For 5 years:
x = 5
y = 360,000(1 - 0.027)^5
y ≈ 360,000(0.973)^5
y ≈ 360,000(0.891)
y ≈ 320,760
After 5 years, the estimated population of Western Lowland Gorillas would be approximately 320,760.
For 10 years:
x = 10
y = 360,000(1 - 0.027)^10
y ≈ 360,000(0.973)^10
y ≈ 360,000(0.816)
y ≈ 293,760
After 10 years, the estimated population of Western Lowland Gorillas would be approximately 293,760.
For 20 years:
x = 20
y = 360,000(1 - 0.027)^20
y ≈ 360,000(0.973)^20
y ≈ 360,000(0.674)
y ≈ 243,840
After 20 years, the estimated population of Western Lowland Gorillas would be approximately 243,840.