Description
A disease arrives, % of infected is max after 8 days. Evaluate for p.
p(t)=9te^-t/8
t=8
how do I evaluate for p?
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Explanation & Answer
So you can verify that max is at t=8 by taking the derivative of p(t) and setting it equal to zero (i.e., calculate t-value where p'(t)=0).
p'(t) = 9*e^(-t/8) + (9t)*(-1/8)*(e^(-t/8)) = 9*e^(-t/8)*(1-t/8)
For max, set p'(t) = 0; thus t=8
Now, we just need to plug t=8 into the original equation for p(t);
Thus: p(8) = 9*8*e^(-8/8) = 9*8/e = 72/e (or aprox., 26.4873)
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Rest of the problems are in the attached file. I also attached book.1.(the Exchange Paradox) You’re playing the following game against an opponent,
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this problem, but when the game is played the envelopes have no markings on them), and (without
you or your opponent seeing what she does) she puts $m in envelope 1 and $2 m in envelope 2 for
some m > 0 (treat m as continuous in this problem even though in practice it would have to be
rounded to the nearest dollar or penny). You and your opponent each get one of the envelopes
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reason that if you trade, you will get either $ x
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2 . This makes the
expected value of the amount of money you’ll get if you trade equal to
1
2
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1
2
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