Question 140641
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*a}}}




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b)


In this case p=12 and a=100


{{{p=k*a}}} Start with the equation we found earlier


{{{12=k*100}}} Plug in p=12 and a=100



{{{12/100=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*a}}} Go back to the earlier equation



{{{p=0.12*a}}} Plug in the constant of variation {{{k=0.12}}}



{{{p=0.12*2500}}} 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*a}}} (we needed to solve for k first), we were able to find the number of deer on a given portion of land