To estimate animal populations, biologists count the total number of animals in a small section of a habitat. The total population of animals is directly proportional to the size of the habitat (in acres) polled.
a.Write an equation using only one variable that could be used to solve for the constant of variation k.
b.A biologist counted the number of white tail deer in a 100 acre parcel of land in a nature preserve and found 12 deer. Find the constant of variation k.
c.If the entire nature preserve is 2,500 acres, then what is the total white tail deer population in the preserve? Describe how you arrived at your answer.
a. Let's denote the total number of animals as P and the habitat size in acres as H. We are told that the total population is directly proportional to the size of the habitat.
Using this information, we can write a proportionality equation: P = kH, where k is the constant of variation.
b. We are given that the biologist counted 12 deer in a 100 acre parcel. We can plug these values into the equation from part (a) to solve for k.
12 = k * 100
To find k, divide both sides of the equation by 100:
k = 12/100 = 0.12
Therefore, the constant of variation k is 0.12.
c. If the entire nature preserve is 2,500 acres, we can use the equation from part (a) to find the total white tail deer population.
P = kH
P = 0.12 * 2500
P = 300
Therefore, the total white tail deer population in the preserve is 300. We arrived at this answer by using the constant of variation (k) determined in part (b) and multiplying it by the total habitat size (2,500 acres).