SOLUTION: It is a variation function problem, I just couldn't find the best topic. Here is the problem. I know what the answer is and how to get to the answer I just don't know how I got

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Question 438765: It is a variation function problem, I just couldn't find the best topic.
Here is the problem. I know what the answer is and how to get to the answer I just don't know how I got it.
From measurements on many rivers, geographers find that the length of a river that drains a particular "basin" of land is approximately proportional to the 0.6 power of the area of the basin. The Rio Grande is 3034 kilometers long, and drains a basin of about 500,000 square kilometers.
To get the particular equation expressing river length in terms of basin area, I know that the equation is going to be y=k*x^0.6 -> 3034=500000^0.6*k which results with y=1.16*x^0.6.
But why does y have to be 3034? I thought y had to be the dependent variable, and I thought the basin depended on how long the river is, not vice versa.
Also, if the river in the world is the 6700 kilometer Nile, approximatley what area of land does the Nile drain? (still the same question)
I think it is a logs question but how would you solve it?
Thank you!!!!!!! You will be my life-saver ! :D
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+k%2Ax%5E0.6, where y = length of river and x = area of the basin.
==> 3034+=+k%2A500000%5E0.6
==> k+=+3034%2F500000%5E0.6+=+1.1551, to 4 decimal places.
==> y+=+1.1551x%5E0.6
==> for the Nile River 6700 km long,
6700+=+1.1551x%5E0.6
==> x%5E0.6+=+5800.17676
==> x+=+root%280.6%2C+5800.17676%29+ = 1,872,414.726 square kilometers of basin is drained.