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Answer :
In order to determine the amount of tungsten after 147 days, use the following formula for the radioactive decay:
[tex]A=A_oe^{-\lambda t}[/tex]where
A: amount of tungsten after t days
Ao: initial amount of tungsten = 0.725 kg
t: time = 147 days
λ: decay constant
Then, it is necessary to find the value of λ. Use the following formula:
[tex]\lambda=\frac{\ln 2}{t_{\frac{1}{2}}}[/tex]where t1/2 is the half-life of tungsten (69.4 days)
[tex]\lambda=\frac{\ln 2}{69.4}=0.00998[/tex]next, replace the previous result and the values of the other parameters into the formula for A:
[tex]A=(0.725kg)e^{-(0.00998)(147)}=(0.725kg)(0.23)=0.167\operatorname{kg}[/tex]Hence, after 147 days, there are 0.167 kg of tungsten 188
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