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.
Write an equation using only one variable that could be used to solve for the constant of variation k.
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.
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.
To write an equation using only one variable to solve for the constant of variation, we'll use the formula for direct variation, which states that the total population is directly proportional to the size of the habitat:
Population = k * Habitat size
In this case, let's use "P" to represent the population and "H" to represent the habitat size. The equation becomes:
P = k * H
Next, we'll use the information given to solve for the constant of variation, k. We are told that in a 100-acre parcel of land, the biologist counted 12 deer. Substituting these values into the equation, we have:
12 = k * 100
To solve for k, we divide both sides of the equation by 100:
12/100 = k
Simplifying:
0.12 = k
Therefore, the constant of variation is 0.12.
To find the total white-tailed deer population in the entire 2,500-acre nature preserve, we can now use the equation with the calculated value of k:
P = k * H
P = 0.12 * 2500
Simplifying:
P = 300
Therefore, the total white-tailed deer population in the preserve is 300.