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 say the variable representing the total number of animals is "N" and the variable representing the size of the habitat in acres is "A." The equation that could be used to solve for the constant of variation "k" is:
N = kA
b. In this case, we know that when the size of the habitat (A) is 100 acres, the number of white tail deer (N) is 12. Substituting these values into the equation, we can solve for k:
12 = k * 100
k = 12/100
k = 0.12
So the constant of variation "k" is 0.12.
c. To find the total white tail deer population in the preserve, we can use the equation N = kA with the given size of the preserve (A = 2,500 acres) and the constant of variation we found (k = 0.12):
N = 0.12 * 2500
N = 300
Therefore, the total white tail deer population in the preserve is 300. This is derived from multiplying the constant of variation by the size of the preserve in acres.