Question 1198803
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x = number of days
y = amount of radon leftover, in grams
a = starting amount of radon gas = 38 grams
H = half-life of radon gas = 3.82 days


Half-life equation
y = a*(0.5)^(x/H)
y = 38*(0.5)^(x/3.82)


We want to find out the value of x when there are y = 6.8 grams of radon gas leftover.


Use logarithms to help isolate the exponent.
The relevant log rule used will be log(A^B) = B*log(A) to help pull down the exponent and isolate it.


y = 38*(0.5)^(x/3.82)
6.8 = 38*(0.5)^(x/3.82)
6.8/38 = (0.5)^(x/3.82)
0.17894737 = (0.5)^(x/3.82)
Log(0.17894737) = Log( (0.5)^(x/3.82) )
Log(0.17894737) = (x/3.82)*Log(0.5)
3.82*Log(0.17894737) = x*Log(0.5)
x = 3.82*Log(0.17894737)/Log(0.5)
x = 9.48274032162061
x = 9.48


It takes <font color=red>approximately 9.48 days</font> for there to be 6.8 grams of radon gas remaining.
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