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Answer :
In this problem we have a decay exponential function of the form
[tex]y=a(b)^x[/tex]where
a=300 g
so
[tex]y=300(b)^x[/tex]For x=11 min, y=300/2=150 g
substitute
[tex]\begin{gathered} 150=300(b)^{(11)} \\ solve\text{ for b} \\ b^{(11)}=\frac{150}{300} \\ b=\sqrt[11]{\frac{1}{2}} \\ \\ b=(0.5)^{\frac{1}{11}} \end{gathered}[/tex]substitute in the equation
[tex]\begin{gathered} y=300(0.5^{(\frac{1}{11})})^x \\ y=300(0.5^)^{\frac{x}{11}} \end{gathered}[/tex]For y=80 g
substitute and solve for x
[tex]\begin{gathered} 80=300(0.5^)^{(\frac{x}{11})} \\ \frac{80}{300}=(0.5)^{(\frac{x}{11})} \\ apply\text{ log on both sides} \end{gathered}[/tex][tex]log\frac{80}{300}=\frac{x}{11}log(0.5)^[/tex]x=21.0 min
the answer is 21.0 minutes
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