10. If 90 kg of Cobalt 60 decays to 3.9 kg in 24 years, what is the half life?

The correct answer can be found using the formula for radioactive decay:N(t) = N₀ * (1/2)^(t/T)Where:* N(t) is the amount remaining after time t (3.9 kg)* N₀ is the initial amount (90 kg)* t is the elapsed time (24 years)* T is the half-life (what we want to find)Let's plug in the values and solve for T:3.9 = 90 * (1/2)^(24/T)Divide both sides by 90:3.9/90 = (1/2)^(24/T)0.04333 = (1/2)^(24/T)Now, take the logarithm base (1/2) of both sides:log_(1/2)(0.04333) = 24/TOr, using the property of logarithms, we can use log base 10 or the natural logarithm (ln):ln(0.04333) / ln(1/2) = 24/T-3.140 = 24/TNow, solve for T:T = 24 / -3.140 * -1T ≈ 4.59 yearsTherefore, the half-life of Cobalt-60 is approximately 4.59 years.