Answer:
25.48 days
Step-by-step explanation:
For a radioactive substance, the Amount of the substance remaining A(t) is modeled by the equation
[tex]A(t)=A_0(\dfrac{1}{2})^{\dfrac{t}{t_{1/2}} }[/tex]
where
[tex]A_0 =$Initial Amount$\\t_{1/2}=$Half-Life of the Substance$\\t=$Time elapsed$[/tex]
In the given problem:
Half Life of the Radioactive Isotope = 8
Initial Amount, [tex]A_0[/tex]=100%=1
A(t)=11% =0.11
Therefore substituting in the model above:
[tex]0.11=1(\dfrac{1}{2})^{\dfrac{t}{8} }\\0.11=0.5^{t/8}\\$Change to Logarithm form$\\Log_{0.5}0.11=\frac{t}{8}\\\frac{Log 0.11}{Log 0.5} =\frac{t}{8}\\3.1844=\frac{t}{8}\\t=8X3.1844=25.4752[/tex]
The farmer need to wait for 25.48 days
