Answer:
The half-life of the substance is of 1600 years.
Step-by-step explanation:
Amount of the substance:
The amount of the substance after t years is given by the following equation:
[tex]C(t) = A(0.999567)^t[/tex]
In which A is the initial amount.
Find the half-life:
This is t for which [tex]C(t) = 0.5A[/tex], that is, the amount is half the initial amount. So
[tex]C(t) = A(0.999567)^t[/tex]
[tex]0.5A = A(0.999567)^t[/tex]
[tex](0.999567)^t = 0.5[/tex]
[tex]\log{(0.999567)^t} = \log{0.5}[/tex]
[tex]t\log{0.999567} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{0.999567}}[/tex]
[tex]t = 1600[/tex]
The half-life of the substance is of 1600 years.
