Exponential and Logarithmic Functions - Applications of Exponential and Logarithmic Functions

The amount, \(y\) milligrams, of a radioactive substance present after \(t\) years, is given by \(y=A{{\mathrm{e}}^{-0.2t}}\), where \(A\) is a constant. At the beginning of \(2000\), there was an estimated amount of \(500\)mg.

Find

1. the value of \(A\),
2. the amount present in the year \(2005\),
3. the year in which the amount of substance would be expected to be halved.
4. the amount that has decayed after one decade.