3.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.
n = k A
12 = k * 100
so
k = 12/100 = 3/25
n = (3/25) 2500
=300
a. To solve for the constant of variation, we can set up a proportion using the given information. Let's denote the total number of animals in the habitat as P, and the size of the habitat in acres as A. The equation can be written as:
P = k * A
In this equation, k represents the constant of variation.
b. We are given that in a 100 acre parcel of land, there are 12 deer. We can substitute these values into the equation from part (a) to solve for k:
12 = k * 100
To isolate k, we can divide both sides of the equation by 100:
k = 12/100
k = 0.12
So, the constant of variation is 0.12.
c. To find the total white tail deer population in the preserve, we can use the constant of variation we found in part (b) and plug in the size of the entire nature preserve, which is 2,500 acres:
P = k * A
P = 0.12 * 2500
P = 300
Therefore, the total white tail deer population in the preserve is 300. To arrive at this answer, we used the equation involving the constant of variation, substituted the known values, and performed the necessary calculations.