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Answer 1 · 2016-12-08T18:16:29

$Q(62" hours") = 15.45 "g of "^42K$

Using the formula:

$Q(t) = Q(0)e^(alphat)$

Using this reference half-life of $""^42K$ , set $t = 12.36" hours"$ and make $(Q(t))/(Q(0)) = 1/2$ :

$1/2 = e^(alpha(12.36" hours"))$

Use the natural logarithm on both sides:

$ln(1/2) = ln(e^(alpha(12.36" hours")))$

Flip the equation and ln(e) redues to the exponent:

$alpha(12.36" hours") = ln(1/2)$

$alpha(12.36" hours") = -ln(2)$

$alpha = -ln(2)/(12.36" hours"$

$Q(62" hours") = (500 "g of "^42K)e^((-ln(2)/(12.36" hours")(62" hours"))$

$Q(62" hours") = 15.45 "g of "^42K$