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Okay. So for this problem, they give us
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an equation of 10,000 times one minus 0.95 to the
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X power most one over X. And they just
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want to know what X gives us the minimum value
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. So to minimise this s o the average equals
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that this is our objective equation. And we only
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have one variable, so we don't really need constraints
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here. So we take the derivative. It'll have
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the same zero if we drop this 10,000 or not
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. Eso The derivative is just negative. Natural log
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of 0.95 at times 0.95 to the X and that
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minus one over x squared. Okay, In lieu
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of trying to solve this algebraic lee, I just
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grafted to see where it crosses the X axis.
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Um, so just be careful in your in your
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calculators. Um, make sure you put parentheses around
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that natural auger pregnancies around the 0.95 just to make
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sure it doesn't evaluate Natural. Got the whole thing
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. Sometimes calculators can give a hiccup with natural log
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. Um, it crosses the X axis somewhere close
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to fot 5.2 And since the closest group size to
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5.2 is five. Then get with the group size
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of five to have the minimum number of tests,
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and that's all, thank you very much.