SOLUTION: 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 siz

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Question 140641: 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.


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let p=# of animals and a=size of habitat


So if the "total population of animals is directly proportional to the size of the habitat", this means that we have the equation


p=k%2Aa



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b)

In this case p=12 and a=100

p=k%2Aa Start with the equation we found earlier

12=k%2A100 Plug in p=12 and a=100


12%2F100=k Divide both sides by 100 to isolate k

0.12=k Divide


So the constant of variation is k=0.12



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c)

p=k%2Aa Go back to the earlier equation


p=0.12%2Aa Plug in the constant of variation k=0.12


p=0.12%2A2500 Plug in a=2500


p=300 Multiply

So in a 2,500 acre parcel of land, there are 300 deer.

By using the equation p=0.12%2Aa (we needed to solve for k first), we were able to find the number of deer on a given portion of land