SOLUTION: For which value(s) of r does there exist a power function (y= Cx^r) passing through the points (1, 1/8) and (5, 9/2). I tried setting them both equal to C and then solving for r

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Question 350281: For which value(s) of r does there exist a power function (y= Cx^r) passing through the points (1, 1/8) and (5, 9/2).
I tried setting them both equal to C and then solving for r, but the r's cancelled.
Answer by jim_thompson5910(28476) About Me  (Show Source):
You can put this solution on YOUR website!
The point (1, 1/8) means that x=1 and y=1/8. Plug these values in to get 1%2F8=C%281%29%5Er and simplify to get C=1%2F8


So the equation is now y=%281%2F8%29x%5Er.


The point (5, 9/2) means that x=5 and y=9/2. Plug these values in to get 9%2F2=%281%2F8%29%285%29%5Er


Then multiply both sides by 8 to get 36=5%5Er and then solve for 'r' to get r=log%285%2C%2836%29%29