Answer:
Explanation:
a. To model the population of Western Lowland Gorillas after 5, 10 and 20 years, we can use an exponential decay model. This model assumes that the population of the gorillas is decreasing at a constant rate over time.
Let y equal the population of the gorillas and x represent the number of years since 2022.
The exponential decay model is represented by the equation:
y = a*e^(-rt)
Where a is the initial population, r is the decay rate and t is the number of years.
If we assume that the initial population of gorillas in 2022 is 1000, the decay rate is 0.1, and we can calculate the population of gorillas after 5, 10, and 20 years.
For 5 years after 2022:
y = 1000e^(-0.15) = 810 gorillas
For 10 years after 2022:
y = 1000e^(-0.110) = 648 gorillas
For 20 years after 2022:
y = 1000e^(-0.120) = 404 gorillas
b. Table:
Years Gorilla Population
5 810
10 648
20 404
c. The table shows that the population of gorillas is decreasing over time, which is an example of exponential decay. This decrease is consistent with the exponential decay model which we used. Exponential decay models are often used to predict population changes in endangered species as they assume a constant rate of decrease in population. Scientists can use this model to predict future populations, as well as estimate the rate of population decline. Based on this information, conservation efforts can be better planned, and resources can be allocated more effectively to prevent the extinction of endangered species.