4. A common example of exponential decay is radioactive decay. Radioactive materials, and some other substances, decompose according to a formula for exponential decay. That is, the amount of radioactive material A present at time t is given by the formula
A=A₀eᵏᵗ
where k < 0.
A radioactive substance is often described in terms of its half-life, which is the time required for half the material to decompose.
After 500 years, a sample of radium-226 has decayed to 80.4 % of its original mass. Find the half-life of radium-226.