The half-life of the given exponential function is of 346.57 years.
What is the half-life of an exponential function?
It is the value of t when A(t) = 0.5A(0).
In this problem, the equation is:
[tex]A(t) = A(0)e^{-0.002t}[/tex].
In which t is measured in years.
Hence the half-life is found as follows:
[tex]0.5A(0) = A(0)e^{-0.002t}[/tex]
[tex]e^{-0.002t} = 0.5[/tex]
[tex]\ln{e^{-0.002t}} = \ln{0.5}[/tex]
[tex]0.002t = -\ln{0.5}[/tex]
[tex]t = -\frac{\ln{0.5}}{0.002}[/tex]
t = 346.57 years.
More can be learned about exponential functions at https://brainly.com/question/25537936
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