Question

"Coyotes are mammals similar to wolves and dogs that are most commonly found in wild habitats of the western United States. However, they are very adaptable carnivores and now appear in urban areas as far east as Washington, D.C., and New York. There is limited data on the actual numbers of coyotes now living in east coast states, but suppose there are now about 1,500 such animals living in Delaware, Maryland,

1. Assume that the coyote population in these areas increases by 15% per year. What function will predict the population n years from now? Create a graph of your function. Label it f(x).
2. Assume instead that the population increases by 250 coyotes per year. What function will predict the population n years from now? Create a graph of your function. Label it g(x).
3.Coyotes are predators that feed on other wild animals like fox, geese, raccoons, and deer. It might be reasonable to assume that the population of those prey species would be inversely proportional to the population of coyotes. Under that assumption, which of the following functions could provide a model for the relationship between the population of deer d and the population of coyotes c around Washington, D.C., over the next few years? It might help to graph them on your Desmos graph and pick one that "makes sense". Explain why you chose that function.
d(c)=10,000-c
d(c)=10,000c
d(c)=10,000c

Answer 1

The function to predict the population of coyotes n years from now is f(x) = 1500(1 + 15/100)^n. The function to predict the population if it increases by 250 coyotes per year is g(x) = 1500 + 250n. The function that provides a model for the relationship between the population of deer and the population of coyotes is d(c) = 10,000-c.

Step-by-step explanation:

To predict the population of coyotes n years from now, we can use the formula:

f(x) = P(1 + r/100)^n

Here, P represents the initial population, r represents the growth rate (15% in this case), and n represents the number of years. So, the function to predict the population would be:

f(x) = 1500(1 + 15/100)^n

To predict the population if it increases by 250 coyotes per year, we can use the formula:

g(x) = P + mx

Here, P represents the initial population and m represents the rate of increase (250 in this case). So, the function to predict the population would be:

g(x) = 1500 + 250n

Considering that the population of prey species is inversely proportional to the population of coyotes, the function that would provide a model for the relationship between the population of deer (d) and the population of coyotes (c) around Washington, D.C., is:

d(c) = 10,000-c

This function makes sense because as the population of coyotes increases, the population of deer is expected to decrease.