Question 1206895
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Answer:  <font color=red size=4>40.71 years</font>


Explanation


One way to represent the half-life formula is: 
y = A*(0.5)^(x/H)
where,
x = number of years
A = starting amount
H = half-life in years
y = final amount after x years
Optionally you can replace "years" with some other time unit.


Let's isolate H.
y = A*(0.5)^(x/H)
y/A = (0.5)^(x/H)
log( y/A ) = log( (0.5)^(x/H) )
log( y/A ) = (x/H)*log( 0.5 )
H*log( y/A ) = x*log( 0.5 )
H = x*log( 0.5 )/log( y/A )


Plug in x = 30, y = 150, A = 250
You should get the following
H = x*log( 0.5 )/log( y/A )
H = 30*log( 0.5 )/log( 150/250 )
H = 30*log( 0.5 )/log( 0.6 )
H = 40.707463465702 approximately
H = <font color=red size=4>40.71 years</font> is the approximate half-life when rounding to 2 decimal places.
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