Direct/indirect variation: biologists count the total # of animals in a small section of a habitat. The total population is directly proportional to the size of the habitat. Write an equation to solve for the constant of variation 'k.'
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This is translating an English sentence into a mathematical equation. All we're really doing is condensing notation (using fewer symbols).
The total population is directly proportional to the size of the habitat.
The total population = directly proportional to the size of the habitat. (is means "equals")
Population(size of habitat) = directly proportional to the size of the habitat. ( Population is A FUNCTION OF the size of the habitat... meaning you input habitat size, your output is population).
P(h) = directly proportional to the size of the habitat. (Abbreviating "size of habitat" to "h")
P(h) = directly proportional to h (more abbreviation just like before)
P(h) = k * h ("directly proportional to" means "some constant k times...(whatever it's directly proportional to)
So the final equation is
P(h) = k*h
Or something like that. :)
That's similar to what I had, but I was simply using different variables. I still don't quite understand direct and indirect variation.
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Oh, yes. Sorry about that. There's a follow up question asking " A biologist counted 12 deer in a 100 acre parcel of land. Find the constant of variation 'k.'" I don't need the answer so much as I need to know how to work this.
Wait, is the constant of variation going to be k = 3/25?
Oh, that has nothing to do with inverse variation though.
P = 12 deer
h = 100 acres
12 = k*100
solve for k