Question

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.'

Answer 1

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. :)

Answer 2

That's similar to what I had, but I was simply using different variables. I still don't quite understand direct and indirect variation.

Answer 3

Do you mean direct and INVERSE variation?

Answer 4

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.

Answer 5

Wait, is the constant of variation going to be k = 3/25?

Answer 6

Oh, that has nothing to do with inverse variation though.

P = 12 deer
h = 100 acres

12 = k*100
solve for k

Answer 7

Oh good! I did it right. Thanks so much!

Answer 8

Yup k = 3/25 , you got it.