Answer:
We have a formula for decay is:
[tex]y=ab^x[/tex]
We have given that decay of 1/4 that means y becomes a/4
and time is given 3200 years.
Substituting the values we get:
[tex]\frac{a}{4}=a(b)^3200[/tex]
[tex]\Rightarrow (\frac{1}{4})^\frac{1}{3200}=b[/tex]
[tex]b=.9995[/tex]
Now, we have to find when y becomes a/2 we get:
[tex]\frac{a}{2}=a(\frac{1}{4})^\frac{1}{3200})^x[/tex]
[tex]\Rightarrow log(\frac{1}{2})=\frac{x}{3200}log(\frac{1}{4})[/tex]
[tex]\Rightarrow 3200\cdot \frac{log2}{log4}=x[/tex]
[tex]\Rightarrow x=1600[/tex]
Hence, the half life would be 1600
