I have been given a T table. On one side is the A column. It has the values 2, 8 and 50. On the other side is the B column. It has the values 10, 20 and 50, respectfully. I now have to find the equation that relates A to B for this table. The hint is to assume that A=kB^x, and to find k and x. I have no idea how to go about doing any of this. Could anyone give me some guidance to solve this type of problem?
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A = kB^x
So you have 3 equations, based on your 3 data points:
2 = k10^x
8 = k20^x
50 = k50^x
divide the 2nd equation by the first:
8/2 = k20^x / (k10^x)
=> 4 = 20^x / 10^x
=> 4 = (20 / 10)^x
=> 4 = 2^x
=> x = 2
So now you've got:
2 = k(10^2)
8 = k(20^2)
50 = k(50^2)
.... and you should be able to solve it from there
So you have 3 equations, based on your 3 data points:
2 = k10^x
8 = k20^x
50 = k50^x
divide the 2nd equation by the first:
8/2 = k20^x / (k10^x)
=> 4 = 20^x / 10^x
=> 4 = (20 / 10)^x
=> 4 = 2^x
=> x = 2
So now you've got:
2 = k(10^2)
8 = k(20^2)
50 = k(50^2)
.... and you should be able to solve it from there