A deadly virus is carried by a certain kind of mouse which dwells in and about t
ID: 3117155 • Letter: A
Question
A deadly virus is carried by a certain kind of mouse which dwells in and about the floor of a 200 acre old growth forest in the southwestern United States. On the edge of this forest is a small village with a population of 23. When the mouse population gets too large, the mice venture more into the village in search of food and new places to inhabit, thereby spreading their virus and causing villagers to become infected. There is also a certain kind of owl which dwells in this forest, and as we all know, owls love to feast on mice. Since the virus is only harmful to humans, the owls are unaffected. So long as the number of owls stays at a reasonable level, the mice population is kept at a comfortable level and the virus is not transmitted to the villagers. However, visualizing large profits, the owner of the old growth forest begins to sell timber to a large lumber company; this, of course, removes the homes of the owls, and they either die off or must leave in search of other shelter.
The interrelationships of the villagers, virus, mice, owls, trees, and loggers can be described by the following mathematical model.
V – number of cases of virus among the villagers
M – mouse population
W – owl population
T – number of acres of trees remaining
V = 0.025M – 20 (1)
M = 1600 – 20W (2)
W = 0.2T (3)
[a] What are the domain and range of each of these three functions in the model?
Explanation / Answer
V = 0.025M - 20
since the mice population is increasing
the domain of this function is [ 0 , infinity )
village has a population of 23
so range = [ 0 , 23 ]
M = 1600 - 20W
domain is [ 0 , infinity )
range = [ 0 , infinity )
W = 0.2T
number of acres of trees 200
domain is [ 0 , 200 ]
range = [ 0, infinity)