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.
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a. The equation that could be used to solve for the constant of variation, k, is:
Total population = k * Size of the habitat (in acres)
b. To find the constant of variation, k, we can use the given information:
Total population = k * Size of habitat
Number of deer = 12
Size of habitat = 100 acres
Plugging in these values into the equation, we get:
12 = k * 100
To solve for k, divide both sides of the equation by 100:
k = 12/100
k = 0.12
Therefore, the constant of variation, k, is 0.12.
c. To find the total white-tail deer population in the preserve, we use the constant of variation, k, and the size of the entire nature preserve, which is 2500 acres. We can use the equation:
Total population = k * Size of the habitat
Plugging in the values, we get:
Total population = 0.12 * 2500
Total population = 300
Therefore, the total white-tail deer population in the preserve is 300.