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# Calculating percentage tolerance....... watch

1. I have some measurements below:

a1 = 96.0

c1 = 1.25

a2 = 60.0

c2 = 0.50

It is suggested that 'c' is proportional to 'a' cubed. Show whether this is true within a 12% tolerance. I'm not sure how to go about this. I guess you find the constant of proportionality first so:

1.25/96^3 = 1.4 x 10^-6

0.50/60^3 = 2.3 x 10^-6

Can you just add 12% onto the lower number: 1.4 x 10^-6 x 1.15 = 1.61 x 10^-6. Therefore it is not within the tolerance?

Another way I thought would be to use one of the constants calculated and use it to find the expected value in the other set of values:

If we take 1.4 x 10^-6 to calculate the expected value of c2:

c2 = 1.4 x 10^-6 x 60^3 = 0.30

But we know c2 to be 0.50 so then we can do:

(50-30)/30 = 67%

Is that right, that seems really high to me?

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Updated: January 12, 2015
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