can you help me with power functions?

Question

The data table satisfies the equation y=kx to the n power. k and n are positive integers. find k and n
X__2__3___4__5
Y__1_2.25_4__6.25
i am completely lost. any help would be great. thank you.

Answer 1

Pick two points:

1 = k2^n
4 = k4^n

If you divide the second equation by the first:

4/1 = k4^n/k2^n = 2^(2n)/2^n = 2^n

so n = 2.

Then 1 = k2^2 = 4k, so k = 1/4.

Answer 2

Did you mean y=kx^n or y=(kx)^n? [it makes a difference as to what k will be. If the former, k=1/4. If the latter, k=1/2. k cannot be an integer as the problem states.]

In any event, the function is as follows:

y = (x/2)^2
= (1/4)x^2

x = 2, y = (2/2)^2 = 1^2 = 1
x = 3, y = (3/2)^2 = (1.5)^2 = 2.25
x = 4, y = (4/2)^2 = 2^2 = 4
x = 5, y = (5/2)^2 = (2.5)^2 = 6.25