What in the world does this mean?
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.
Hi again Laura: it's putting into words the consequences of one of the assumptions that we made when we worked out the number of animals in that conservation park, namely that the density of animals in a small section of their habitat (in that example that would have been the area of the park where the conservationist took her sample) is the same as the density of animals throughout their habitat (in that example, the habitat was the park as a whole). So if for example you find five deer in an area of 10 hectares, you're assuming that you'll find approximately 50 deer in an area of 100 hectares. (It's important to realise that you ARE making this assumption when you do calculations like this, since if all the deer in the park were in reality all herded together in the one place the sample was taken, the assumption would be completely wrong.)
oooooooooooh ok thank you.
a. To write an equation using only one variable that could be used to solve for the constant of variation k, we can use the formula:
Number of animals = k * Size of habitat
Let's use the variable "n" to represent the number of animals and "h" to represent the size of the habitat. The equation can be written as:
n = k * h
b. We are given that the biologist counted 12 white tail deer in a 100 acre parcel of land. Using this information, we can substitute the values into the equation and solve for the constant of variation k.
12 = k * 100
To find k, we divide both sides of the equation by 100:
12/100 = k
Simplifying further:
0.12 = k
So, the constant of variation k is 0.12.
c. If the entire nature preserve is 2,500 acres, we can use the equation n = k * h to calculate the total white tail deer population in the preserve.
Using the value of k we found in part b (k = 0.12) and the size of the habitat (h = 2,500 acres), we can substitute these values into the equation:
n = 0.12 * 2,500
n = 300
Therefore, the total white tail deer population in the preserve is 300. To arrive at this answer, we multiplied the constant of variation k (0.12) by the size of the habitat (2,500 acres).